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FOUR PLACE TABLES
OF LOGARITHMS
AND TRIGONOMETRIC
FUNCTIONS
Abridged Edition
compiled by -
E. V. HUNTINGTON
ASSISTANT PROFESSOR OF MATHEMATICS IN HARVARD UNIVERSITY
tº e
º
G. &
O • * *, *
6 º' &
*... ." ... • ,
CONTENTS
I. NATURAL VALUES of THE TRIGONoMETRIC FUNCTIONS (the angles
being given in degrees and decimal parts of a degree).
Sines and cosines. Tangents and cotangents. Secants and cosecants.
II. LoGARITHMS OF NUMBERs.
III. LoGARITHMs of THE TRIGONoMETRIC FUNCTIONS (the angles being
given in degrees and decimal parts of a degree).
Log sin and log cos. Log tan and log cotan.
IV. CoNDENSED TABLE OF THE TRIGONOMETRIC FUNCTIONs.
CopyRIGHT, 1907, BY E. V. HUNTINGTON
For SALE By
THE HARVARD COOPERATIVE SOCIETY
CAMBRIDGE, MASSACHUSETTS


PRICE, 35 CENTS
\mº TT
From Minutes and S600nds into
Decimal Parts of a Degree
(The last figure repeats indefinitely)
From Decimal Parts of a Degree into Minutes
and S600nds. – (Exact Values)
0’=0°.000 || 30’=0°.500
1’ .016 || 31’ .516
2’ .033 || 32’ .533
3’ .050 | 33’ .550
4./ .066 || 34' .566
5’ .083 35’ .583
6/ ..100 36’ .600
7, .116 37’ .616
8’ .133 || 38’ .633
9’ .150 || 39” .650
10^-0°.166 | 40’=0°.666
11” .183 || 41’ .683
12” .200 || 42' .700
13” .216 || 43’ .716
14” .233 44’ .733
15’ .250 || 45’ .750
16” .266 46’ .766
17' .283 || 47' .783
18’ .300 || 48’ .800
19° .316 || 49’ .816
20/=0°.333 || 50'-0°.833
21” .350 || 51’ .850
22’ .366 52’ .866
23’ .383 || 53’ .883
24” .400 54’ .900
25' .416 55 * .916
26’ .433 56’ .933
27' .450 || 57’ .950
28’ .466 || 58’ .966
29* .483 || 59’ .983
30’-0°.500 60’-1°.000
1/4"–157–0°.00416
1/2"–30°–0°.00833
3/4'−45"–0°.01250
10’’=0°.00277
207–0°.00555
30’’=0°.00833
40"—0°.01111
50” = 0°.01388
6”–0°.00166
77–0°.00194
8’’=0°.00222
9"—0°.00250
1 radian=57°.29578–
1°=0.01745329-–padians
1’=0.000290888–H
1"=0.00000484814–
0°.00 = 0’
.01 0’36”
.02 1/12"
.03 1/48"
.04 2^24”
.05 3’
.06 3'36."
.07 4 '12"
.08 4'48"
.09 5’24”
0°.10= 6’
.11 6'36”
.12 7/12”
.13 7 '48"
.14 8'24”
.15 9’
.16 9'36”
.17 10^12”
.18 10^48”
.19 11 "24"
0°.20=12’
.21 12'36”
.22 13 '12"
.23 13 '48"
.24 14 (24”
.25 15 *
.26 15 '36”
.27 16/12"
.28 16’48”
.29 1724”
0°.30=18’
.31 18736"
.32 19712"
.33 19 '48"
.34 20'24”
.35 21 ''
.36 21 '36”
.37 22 '12"
.38 22'48"
.39 23'24”
0°.40=24”
.41 24/36."
.42 25 (12”
.43 25 /48”
.44 26’24”
.45 27’
.46 27'36”
.47 28 (12”
.48 28/487
.49 29'24”
0°.50=30’
0°.50=30’
.51 30 (36”
.52 31 /12”
.53 31'48"
.54 32 /24”
.55 33’
.56 33 (36'
.57 347.2”
.58 34'48"
.59 35 (24”
0°.60=36’
.61 36'36"
.62 37/12"
.63 37 (48"
.64. 38'24"
.65 39’
.66 39 (36"
.67 40/12"
.68 40'48"
.69 41 (24"
0°.70=42^
.71 42 (36."
.72 43 /12"
.73 43'48"
.74 44 (24”
.75 45"
.76 45 /36"
.77 46 (12”
.78 46'48"
.79 47/24"
0°.80=48’
.81 48 (36"
.82 49 (12”
.83 49'48"
.84 50'24”
.85 51*
.86 51 /36”
.87 52 /12"
.88 52'48"
.89 53'24”
0°.90=54’
.91 54'36”
.92 55 (12"
.93 55'48"
.94 56'24”
.95 57
.96 57'36”
.97 58'12"
.98 58 (48"
.99 59'24”
19.00 = 60’
°.000– 0”
°.001.= 3".6
°.002= 7".2
°.003=10".8
°.004– 14”.4
°.005=18".
°.006–21”.6
°.007–25".2
°.008–28”.8
°.009–32”.4
°.01 =36”.


... ', , , Ø, Æ, Å, , , EXPLANATION OF TABLES
* { ..., *; 2.
if -
º:
**
...' , -º __:: *
* 2 ºf t
T roughout this table, angles are expressed in degrees and tenths and hundredths
of a degree instead of in degrees, minutes, and seconds. This plan obviously
simplifies the computation whenever the angles are given decimally; and even when
the angles are not given decimally (see conversion table on opposite page), it will
usually effect a saving of time. .."
The first figures of the angle are given at the side of the page, and the last figure
along the top. All the values of any one junction, from 0° to 90°, will be found at one
opening of the book; and on every page the function increases reading forward, and
decreases reading backward.
The first figure of the function is expressed (in general) only in the first and
last columns; a point at which the first figure changes is indicated by the sign ſ.
The negative characteristics, 1, 2, etc., may be modified into 9–10, 8–10, etc.,
if preferred.
To facilitate interpolation the “tenths of the tabular differences” are given at the
end of each line in the main part of the table (as in J. M. Peirce's table of logarithms
of numbers). In using these aids always find first the nearest tabular entry, and
then add or subtract as the case may require; and notice that, since the tenths of the
difference are directly given, the actual size of the difference itself need not be con-
sidered.
Thus, to find log tan 36°.87. The nearest entry in the table is log tan 369.9 =T.8755; since the
given angle is three tenths of the way toward the adjacent angle on the left, the required logarithm
is (approximately) three tenths of the way toward the adjacent logarithm; but by the marginal
table, three tenths of this interval in 5 units in the last place; hence, the required logarithm is 1.8750
(which may also be written 0.8750 — 1, or 9.8750 – 10).
Again, to find the angle a when ctn a = 1.3333. The nearest entry in the table is 1.3319 =
ctn 36°.9; the given function differs from this by 14 units in the last place, which, by the marginal
table, is three tenths of the way toward the adjacent function; therefore the required angle is
(approximately) three tenths of the way toward the adjacent angle, and is a = 36°.87.
Any interpolated value may be in error by one unit in the last place; the parts of
the table where the errors of interpolation may be greater than this are indicated in
the margin. Practice in ordinary interpolation without marginal aids may be
obtained from the latter part of the tables of natural tangents and secants.
Marginal tabs are provided throughout the table; in using them, put the thumb
on the desired tab, and throw the free pages over; do not insert the fingers under
these tabs.
In the logarithmic part of the table, the special tabs at the upper and lower edges
of the page make it possible to manipulate the table entirely with the left hand, the
book lying flat on the desk; to turn forward, insert the thumb under the required
tab at bottom of page; to turn backward, insert the fingers under the required tab
at top of page.


NG- L^T
Sine Cosime
... *-*—º-Z & 3 2 ..] () nº
0 1 2 3 4 .7 .5Tā-l 1 2 3 4 5
0.000000| 90°
#
#
0° | 0000000 001745 003491 005235 008081 008727 010472 012217 018852 015707 017452| 89 |175349524608873
l 01745 01920 02094 02269 02443 02618 02792 02967 03141 03316 03490 88 17 35 52 70 87
2 03490 03664 03839 04013 04188 04362 04536 04711 04385 05059 05234 || 87 || 17 35 52 70 87
3 05234 05408 05582 05756 05931 06105 06279 06453 06627 06802 06976 86 || 17 35 52 70 87
4 06976 07150 07324 07498 07672 07846 08020 03194 08368 03542 08716 85 || 17 35 52 70 87
5 0.8716 0.8889 09063 09237 0941 1 09585 09758 09932 10106 10279 10453 84 || 17 35 52 69 87
6 10453 10626 10800 10973 11147 11320 11494 11657 11840 12014 12187 83 || 17 35 52 69 87
7 12187. 12360 12533 12706 12880 13053 13226 13399 13572 13744 13917 82 || 17 35 52 69 87
8 13917 14090 14263 14436 14608 14781. 14954 15126 15299 15471 15643 81 || 17 35 52 69 86
9 15643 15816 15988 16160 16333 16505 16677 16849 17021 17193 0.17365 || 30° | 17 34 52 69 86
10° | 0.1736 1754 1771 1788 1805 1822 1840 1857 1874 1891 1908 79
11 1908 1925 1942 1959 1977 1994 2011 2028 2045 2062 2079 78
12 2079 2096 2113 2130 2147 2,164 218.1 2198 2215 2233 2250 77
13 2250 2267 2284 2300 2317 2334 2351 2368 2385 2402 2419 || 76
14 2419 2436 2453 2470 2487 2504 2521. 2538 2554 2571 2588 75
15 2588 2605 2622 2639 2656 2672 2689 2706 2723 2740 2756 || 74
16 2756 2773 2790 2807 2823 2840 2857 2874 2890 2.907 2924 || 73
17 2924 2940 2957 2974. 2990 3007 3024 3040 3057 3074 3090 || 72
18 3090 3107 3123 3140 31.56 3173 3190 3206 3223 3239 3256 || 71
19 3256 3272 3289 3305 3322 3338 3355 3371 3387 3404 0.3420 || 70°
20° | 0.3420 3437 3453 3469 3486 3502 3518 3535 3551 3567 3584 || 69
21 3584 3600 3616 3633 3649 3665 3681 3697 3714 3730 3746 | 68
22 3746 3762 3778 3795 3811 3827 3843 3859 3875 3891 3907 || 67
23 3907 3923 3939 3955 3971 3987 4003 4019 4035 4051 4067 | 66
24 4067 4083 4099 4115 4131 4147 4163 4179 4195 4210 4226 || 65
25 4226 4242 4258 4274 4289 4305 4321 4337 4352 4368 4384 || 64
26 4384. 4399 4415 4431 4446 4.462 4478 4493 4509 45.24 4540 || 63
27 4540 4555 4571 4586 4602 4617 4633 4648 4664 4679 4695 62
28 4695 4710 4726 4741 4756 4772 4787 4802 4818 4833 4848 || 61
29 4848 4863 4879 4894 4909 4924 4939 4955 4970 4985 0.5000 || @@9
30° 0.5000 5015 5030 5045 5060 5075 5090 5105 5120 5135 5150 | 59
31 5150 5165 5180 5.195 5210 5225 5240 5.255 5270 528.4 5299 || 58
32 5299 5314 5329 5344 5358 5373 5388 5402 5417 5432 5446 || 57
33 5446 5461 5476 5490 5505 5519 5534 5548 5563 5577 5592 || 56
34 5592 5606 5621 5635 5650 5664 5678 5693 5707 5721 5736 || 55
35 5736 5750 5764 5779 5793 5807 5821 5835 5850 5864 5878 || 54
36 5878 5892 5906 5920 5934 5948 5962 5976 5990 6004. 6018 || 53
37 6018 6032 6046 6060 6074 6088 6101 6115 6129 6143 6157 || 52
38 6157 6170 6184 6198 6211 6.225 6239 62.52 6266 6280 6293 51
39 6293 6307 6320 6334 6347 6361 6374 6388 6401 6414 0.6428 || 50°
40° l 0.6428 6441 6455 6468 6481 6494 6508 6521 6534 6547 6561 || 49
41 6561 6574 6587 6600 6613 6626 6639 6652 6665 6678 6691 || 48
42 6691 6704 6717 6730 6743 6756 6769 6782 6794 6807 6820 || 47
43 6820 6833 6845 6858 6871 6884 6896 6909 6921 6934 6947 || 46
44 6947 6959 6972 6984 6997 7009 7022 7034 7046 7059 0.7071 || 45°
45° | 0.7071


(8)
TU ºr
Sine Cosime
0 #–4–7–0–5 4 3 l () *
—º: .1 2 3 4 5 6-7 .5T 1 2 3 4 5
0.7071 45°
45° I 0.7071 7083 7096 7108 7120 7133 7145 7157 7169 7181 7193 || 44
46 71.93 7206 7218 7230 7242 7254. 7266 7278 7290 7.302 7314 || 43
47 7314 7325 7337 7349 7361 7373 7385 7396 7408 7420 7431 || 42
48 7431 7443 7455 7466 7478 7490 7501 7513 7524. 7536 7547 || 41
49 7547 7559 7570 7581 7593 7604 7615 7627 7638 7649 7660 40°
50° | 0.7660 7672 7683 7694 7705 7716 7727 7738 7749 7760 0.7771 39
51 7771 7782 7793 7804 7815 7826 7837 7848 7859 7869 7880 38
52 7880 7891 7902 7912 7.923 7934 7944 7955 7965 7976 7986 || 37
53 7986 7997 8007 8018 8028 8039 8049 8059 8070 8080 8090 || 36
54 8090 8100 8111 8121 8131 8141 8151 8161 8171 8181. 8192 || 35
55 8192 8202 8211 8221 8231 8241 8251 8261 8271 8281 8290 || 34
56 8290 8300 8310 8320 8329 8339 8348 8358 8368 8377 8387 33
57 8387 8396 8406 8415 8425 8434 8443 8453 8462 8471 84.80 || 32
58 8480 8490 8499 8508 8517 8526 8536 8545 8554 8563 85.72 || 31
59 8572 8581 8590 8599 8607 8616 8625 8634 8643 8652 0.8660 || 30°
60° l 0.8660 8669 8678 8686 8695 8704 8712 8721 8729 8738 8746 || 29
61 8746 8755 8763 8.771 8780 8788 87.96 8805 8813 8821 8829 || 28
62 8829 8838 8846 8854 8862 8870 8878 8886 8894 8902 8910 || 27
63 8910 8918 8926 8934 8942 8949 8957 8965 8973 8980 8988 || 26
64 8988 8996 9003 9011 9018 9026 9033 9041 9048 9056 9063 || 25
65 9063 9070 9078 9085 9092 9100 9107 91.14 9121 9128 9135 | 24
66 9135 9143 9150 9157 9164 91.71 91.78 9184 9191 9198 9205 || 23
67 9205 92.12 9219 9225 92.32 92.39 9245 92.52 92.59 92.65 9272 22
68 9272 9278 92.85 92.91 92.98 9304 9311 9317 9323 9330 9336 || 21
69 9336 9342 9348 9354 936l 9367 93.73 93.79 9385 9391 0.9397 || 20°
70° l 0.9397 9403 9409 94.15 9421 9426 9432 9438 94.44 9449 9455 19
71 9455 9461. 9466 9472 9478 94.83 9489 9494. 9500 9505 9511 18
72 9511 95.16 95.21 9527 9532 95.37 9542 9548 9553 95.58 9563 17
73 9563 9568 9573 9578 95.83 9588 9593 9598 9603 9608 96.13 | 16
74 96.13 96.17 9622 9627 9632 9636 9641 9646 9650 9655 9659 15
75 9659 9664. 9668 9673 9677 9681 9686 9690 9694 9699 97.03 || 14
76 97.03 97.07 9711 9715 9720 9724. 9728 97.32 97.36 97.40 9744 || 13
77 9744 97.48 9751 97.55 97.59 9763 9767 9770 97.74 97.78 9781 12
78 9781 9785 9789 9792 9796 9799 9803 9806 9810 98.13 9816 || 11
79 98.16 9820 9823 9826 9829 9833 9836 9839 9842 9845 0.9848 || 10°
80° | 0.9848 9851 9854 98.57 9860 98.63 9866 9869 9871 9874 9877
81 9877 9880 9882 9885 9888 98.90 9893 98.95 9898 9900 9903
82 9903 9905 9907 9910 9912 9914 99.17 9919 992.1 99.23 99.25
83 9925 9928 9930 9932 9934 9936 9938 9940 9942 99.43 9945
84 9945 99.47 99.49 9951 9952 9954 9956 9957 9959 9960 9962
85 9962 9963 9965 9966 9968 9969 9971 9972 9973 99.74. 9976
86 9976 9977 99.78 9979 99.80 9981 9932 9983 9984 9985 9986
87 9986 9987 9988 9989 9990 9990 99.91 9992 9993 9993 9994
88 99.94 9995 9995 9996 9996 9997 9997 9997 9998 9998 0.9998
89 0.9998 9999 9999 9999 9999 ſ 0000 0000 0000 0000 0000 1.0000
90° | 1.0000
#


(9)
Tangent Cotangent
- LTETTE Tºnths ºf the
- 0 .9) Z—& 5 # 3 2 l () Tabulaſ Diff}IBMCG
–3 1 2 3T4 5 6T-7-ā-ā- 1 2 3 4 5
0.000000 || 90°
0° I 0.000000 001745 003491 005235 008081 008727 010472 012218 018964 Olš709 017455 | 89 |175349524608873
l 0.1746 01920 02095 02269 02444 0.2619 02793 02968 03143 03317 03492 || 88 || 17 35 52 70 87
2 0.3492 03667 03842 04016 04191 04366 04541 04716 04891 05066 05241 || 87 || 17 35 52 70 87
3 05241 05416 05591 05766 05941 06116 06291 06467 06642 06817 06993 || 86 18 35 53 70 88
4 06993 07168 07344 07519 07695 07870 08046 08221 08397 08573 08749 || 85 18 35 53 70 88
5 08749 08925 09101 09277 09453 09629 09805 09981 10158 10334 10510 || 84 18 35 53 70 88
6 10510 10687 10363 11040 11217 11394 11570 11747 11924 12101 12278 || 83 || 18 35 53 71 88
7 12278 12456 12633 12810 12938 13165 13343 13521 13698 13876 14054 || 82 | 18 36 53 71 89
8 14054 14232 14410 14588 14767 14945 15124 15302 15481 15660 15838 || 81 | 18 36 54 71 89
9 15838 16017 16196 16376 16555 16734 16914 17093 17273 17453 0.17633 || 30° | 18 36 54 72 90
10° 0.1763 1781 1799 1817 1835 1853 1871 1890 1908 1926 1944 || 79 || 2 4 5 7 9
ll 1944 1962 1980 1998 2016 2035 2053 2071 2089 2107 2126 || 78 || 2 4 5 7 9
12 2126 2.144 2162 2180 2199 2217 2235 2254 2272 2290 2309 || 77 || 2 4 5 7 9
13 2309 23.27 2345 2364 2382 2401 2419 2438 2456 2475 2493 || 76 || 2 4 6 7 9
14 2493 2512 2530 2549 2568 2586 2605 2623 2642 266l 2679 || 75 || 2 4 6 7 9
15 2679 2698 27.17 2736 2754 2773 2792 2811 2830 2849 2867 || 74 || 2 4 6 8 9
16 2867 2886 2905 2924 2943 2962 2981 3000 3019 3038 3057 | 73 || 2 4 6 8 9
17 3057 3076 3096 31.15 3134 3153 3172 3191 3211 3230 3249 || 72 || 2 4 6 8 10
18 3249 3269 3288 3307 3327 3346 3365 3385 3404 3424 3443 || 71 || 2 4 6 8 10
19 3443 3463 3482 3502 3522 3541 3561 3581 3600 3620 0.3640 || 70° | 2 4 6 8 10
20° | 0.3640 3659 3679 3699 3719 3739 3759 3779 3799 3819 3839 || 69 || 2 4 6 8 10
21 3839 3859 3879 3899 3919 3939 3959 3979 4000 4020 4040 | 68 || 2 4 6 8 10
22 4040 4061 4081 4101 4122 4142 4163 4183 4204 4224. 4245 || 67 || 2 4 6 8 10
23 4245 4265 4286 4307 4327 4348 4369 4390 44.11 4431 4452 | 66 || 2 4 6 8 10
24 4452 4473 4494 4515 4536 4557 4578 4599 4621 4642 4663 || 65 || 2 4 6 8 11
25 4663 4684 4706 4727 4748 4770 4791 4813 4834 4856 4877 || 64 || 2 4 6 9 11
26 || 4877 4899 4921 4942 4964 4986 5008 5029 5051 5073 5095 || 63 || 2 4 7 9 ll
27 5095 5117 5139 5161 518.4 5206 5228 5250 5272 5295 5317 | 62 || 2 4 7 911
28 5317 5340 5362 5384 5407 5430 5452 5475 5.498 5520 5543 .61 || 2 5 7 9 11
29 5543 5566 5589 5612 5635 5658 5681 5704 5727 5750 0.5774 (60° || 2 5 7 9 12
30° | 0.5774 5797 5820 5844 5867 5890 5914 5938 5961 5985 6009 || 59 || 2 5 7 9 12
31 6009 6032 6056 6080 6104 6128 6152 6176 6200 6224 6249 || 58 || 2 5 7 10 12
32 6249 6273 6297 6322 6346 6371 6395 6420 6445 6469 6494 || 57 || 2 5 7 10 12
33 6494 6519 6544 6569 6594 6619 6644 6669 6694 6720 6745 || 56 || 3 5 8 10 13
34 6745 6771 6796 6822 6847 6873 6899 6924 6950 6976 7002 || 55 || 3 5 8 10 13
35 7002 7028 7054 7080 7107 7133 7159 7186 7212 7239 7265 54 || 3 5 8 11 13
36 7265 7292 7319 7346 7373 7400 7427 7454. 7481 7508 7536 || 53 || 3 5 8 11 14
37 7536 7563 7590 7618 7646 7673 7701 7729 7757 7785 7813 || 52 || 3 6 8 11 14
38 7813 7841 7869 7898 7926 7954. 7983 8012 8040 8069 8098 || 51 || 3 6 9 11 14
39 8098 8127 8156 8185 8214 8243 8273 8302 8332 8361 0.8391 || 50° | 3 6 9 12 15
40° l 0.8391 8421 8451 8481 8511 8541 8571 8601 8632 8662 8693 l 49 || 3 6 9 12 15
41 8693 8724 8754 8785 8816 8847 8878 8910 8941 8972 9004 || 48 || 3 6 9 12 16
42 9004 9036 9067 9099 9131 91.63 9.195 9228 9260 92.93 9325 || 47 || 3 6 10 13 16
43 9325 9358 9391 9424 94.57 9490 9523 95.56 9590 9623 0.9657 || 46 || 3 7 10 13 17
44 || 0.9657 9691 9725 97.59 9793 9827 9861 9896 9930 9965ſ 1.0000 || 45° | 3 7 10 1417
45° | 1.0000



(10)
Tangent Coſtangemſt
..& ...} B f th9
f |→–& iſ (§ 5 4. 3 2 l (0) *
0 1 2 3 4TBT.5-i-º-º:- 1 2 3 4 5
1.0000 || 45°
45° | 1.0000 0035 0070 0105 0141 0176 0212 0247 0283 0319 0355 || 44 || 4 7 11 14 18
46 || 0355 0392 0428 0464 0501 0538 0575 0612 0649 0686 0724 || 43 || 4 7 11 15 18
47 0724 0761 0799 0837 0875 0913 0951 0990 1028 1067 1106 || 42 || 4 8 11 15 19
48 1106 1145 1184 1224 1263 1303 1343 1383 1423 1463 1504 || 41 || 4 8 12 16 20
49 1504 1544 1585 1626 1667 l708 1750 1792 1833 1875 1.1918 || 40° || 4 8 12 1721
50° | 1.1918 1960 2002 2045 2088 2131 2174 2218 2261 2305 2349 || 39 || 4 9 13 1722
51 2349 2393 2437 2482 2527 2572 26.17 2662 2708 2753 2799 || 38 || 5 914 18 23
52 2799 2846 2892 2938 2985 3032 3079 3127 3175 3222 3270 || 37 || 5 9 14 19 24
53 3270 3319 3367 3416 3465 3514 3564 3613 3663 3713 3764 || 36 || 5 10 15 20 25
54 3764 3814 3865 3916 3968 4019 4071 41.24 4176 42.29 4281 || 35 || 5 10 16 21 26
55 4281 4335 4388 4442 4496 4550 4605 4659 4715 4770 4826 || 34 || 5 11 1622 27
56 4826 4882 4938 4994 5051 5108 5166 5224 5282 5340 5399 || 33 || 6 11 l'723 29
57 5399 5458 55.17 5577 5637 5697 5757 5818 5880 5941 6003 || 32 || 6 12 18 24 30
58 6003 6066 6128 6.191 6255 6319 6383 6447 6512 6577 6643 || 31 || 6 13 19 26 32
59 6643 6709 6775 6842 6909 6977 7045 7113 7182 7251 1,7321 || 30° || 7 14:20 27 34
60° | 1.7321 7391 7461 7532 7603 7675 7747 7820 7893 7966 8040 || 29 70–74
61 8040 8115 8.190 8265 8341 84.18 8495 85.72 8650 8728 8807 || 28 75–79
62 8807 8887 8967 9047 9128 9210 9292 93.75 9458 95.42 1.9626 || 27 80–84
63 | 1.9626 9711 9797 9883 9970 ſ 0057 0145 0233 0323 0413 2.0503 || 26 85–90
64 || 2.0503 0594 0686 0778 0872 0965 1060 1155 1251 1348 1445 || 25 91–97
65 1445 1543 1642 1742 1842 1943 2045 2148 2251 2355 2460 24 || 3 98–105
66 2460 2566 2673 2781 2889 2998 3109 3220 3332 3445 3559 || 23 # 106–114
67 3559 3673 3789 3906 4023 4142 4262 4383 4504 4627 4751 22 # 114–124
68 4751 4876 5002 5129 5257 5386 5517 5649 5782 5916 6051 | 21 |e 125–135
69 6051 6187 6325 6464 6605 6746 6889 7034 7.179 7326 2.7475 20° = 136–149
70° | 2.7475 7625 7776 7929 8083 8239 8397 8556 8716 8878 2.9042 | 19 |# 150–164
71 || 2.9042 9208 9375 9544 9714 9887 ſ 0061 0237 0415 0595 3.0777 | 18 166–182
72 || 3.0777 0961 1146 1334 1524 1716 1910 2106 2305 2506 2709 || 17 184—203
73 2709 2914 3122 3332 3544 3759 3977 4197 4420 4646 4874 || 16 205—228
74 4874 5105 5339 5576 5816 6059 6305 6554 6806 7062 3.7321 || 15 231–259
75 || 3.7321 7583 7848 8118 8391 8667 8947 9232 9520 9812|4,0108 || 14 262––296
76 || 4.0.108 0408 0713 1022 1335 1653 1976 2303 2635 2972 3315 || 13 | T
77 3315 3662 4015 4374 4.737 5107 5483 5864 6252 6646 4.7046 || 12
78 || 4.7046 7453 7867 8288 8716 9152 9594 ſoo45 0504 0970 5.1446 || 11
79 || 5.1446 1929 2422 2924 3435 3955 4486 5026 5578 6140 5.6713 || 10°
80° 5.6713 7297 7894 8502 9124 9758 ſ 0405 1066 1742 2432 6.3138 9 Interpolation
31 || 6.3138 3859 4596 5350 6122 6912 7720 8548 9395 ſo264 7.1154 8 ACCuſatº, BXGBpt
82 || 7.1154 2066 3002 3962 4947 5958 6996 8062 9158 ſo285 8.1443 7 th9 as figurð
83 || 8.1443 2636 3863 5126 6427 7769 91.52ſ O579 2052 3572 9.5144 6
84 9,514 9,677 9,845 10,019 10,199 10,385 10,579 10,780 10,988 11,205 11,430 5
85 11,430 11,664 11.909 12,163 12,429 12.706 12.996 13,300 13,617 13.951 14.301 4
86 14,301 14,669 15,056 15,464 15,895 16,350 16,832 17,343 17,886 18,464. 19,081 3
87 19,081 19,740 20,446 21,205 22,022 22,904 23,859 24,898 26,031 27,271 28,636 2 Thºmatiºn"
88 28,838 30,145 31.821 33,594 35.801 38,188 40,917 44.066 47.740 52,081 57.290 l ſiſt AGG|Iſatº
89 57.290 63,657 71.615 81,847 95,489 114,59 143,24 190,98 286.48 572.96 co O9
90° CO


(11)
Secant - Cosecant
0 Ti 3-à-4–5–4–4–4 || 0 |º:
1 2 3 4 5
1.0000 || 90°
0° | 1.0000 0000 0000 0000 0000 0000 0001 0001 0001 0001 0002 | 89
l 0002 0002 0002 0003 0003 0003 0004 0004 0005 0006 0006 || 88
2 0006 0007 0007 0008 0009 0010 0010 0011 0012 0013 0014 || 87
3 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 || 86
4 0024 0026 0027 0028 0030 0031 0032 0034 0035 0037 0038 || 85
5 0038 0040 0041 0043 0045 0046 0048 0050 0051 0053 0055 | 84
6 0055 0057 0059 OO61 0063 0065 0067 0069 0071 O073 0075 || 83
7 0075 0077 0079 0082 0084 0086 0089 0091 0093 0096 0098 || 82
8 . I 0098 0.101 0103 0106 0108 01.11 OL14 0116 0119 O122 0125 || 81
9 0.125 0127 0.130 0133 0.136 0139 0.142 0145 0148 0151 1.0154 || 80°
10° | 1.0154 0157 0161 0164 0167 0170 0174 0177 0180 0184 0187 || 79
ll 0187 0191 0194 Olg8 0201 0205 0209 0212 0216 0220 0223 78
12 0223 0227 0231 0235 0239 0243 0247 0251 0255 02:59 0263 || 77
13 0263 0267 0271 0276 0280 0284 0288 0293 0297 0302 0306 || 76
14 0306 0311 0315 0320 0324 0329 0334 0338 0343 0348 0353 || 75
15 0353 0358 0363 0367 0372 0377 0382 0388 0393 0398 0403 || 74
16 0403 0408 0413 0419 0424 0429 0435 0440 0446 0451 0457 | 73
17 0457 0463 0468 0474 0480 0485 0491 0497 0503 0509 0515 || 72
18 0515 0521 0527 0533 0539 0545 0551 0557 0564 0570 0576 || 71
19 0576 0583 0589 0595 0602 0608 0615 0622 0628 0635 1.0642 || 70°
20° | 1.0642 0649 0655 0662 0669 0676 0683 0690 0697 0704 0711 || 69
21 0711 0719 0726 0733 0740 0748 0755 0763 0770 0778 0785 | 68
22 0785 0793 0801 0808 0816 0824 0832 0840 0848 0856 0864 || 67
23 0.864 0872 0880 0888 0896 0904 0913 0921 0929 0938 0946 | 66
24 0946 0955 0963 0972 0981 0989 0998 1007 1016 1025 1034 || 65
25 1034 1043 1052 1061 1070 1079 1089 1098 1107 11.17 1126 64
26 1126 1136 1145 1155 1164. 1174 1184 1194 1203 1213 1223 63
27 1223 1233 1243 1253 1264. 1274 1284 1294 1305 1315 1326 62
28 1326 1336 1347 1357 1368 1379 1390 1401 1412 1423 1434 61
29 1434 1445 1456 1467 1478 1490 1501 1512 1524 1535 l.1547 | (60°
30° | 1.1547 1559 1570 1582 1594 1606 1618 1630 1642 1654 1666 | 59
31 1666 1679 1691 1703 1716 1728 1741 1753 1766 1779 1792 58
32 1792 1805 1818 1831 l;844. 1857 1870 1883 1897 1910 1924 57
33 1924, 1937 1951 1964. 1978 1992 2006 2020 2034 2048 2062 56
34 2062 2076 2091. 2105 2120 2134 2149 2163 2178 2193 2208 55
35 2208 2223 2238 2253 2268 2283 2299 2314 2329 2345 2361 54
36 2361 2376 2392 2408 2424. 2440 2456 2472 2489 2505 2521 53
37 2521. 2538 2554 2571 2588 2605 2622 2639 2656 2673 2690 52
38 2690 2708 2725 2742 2760 2778 2796 2813 2831 2849 2868 51
39 2868 2886 2904 2923 2941 2960 2978 2997 3016 3035 1.3054 || 50°
40° | 1.3054 3073 3093 3112 3131 3151 3171 3190 3210 3230 3250 49 8 10
41 3250 3270 3291 3311 3331 3352 3373 3393 3414 3435 3456 48 8 10
42 3456 3478 3499 3520 3542 3563. 3585 3607 3629 3651 3673 47 9 ll
43 3673 3696 3718 3741 3763 3786 3809 3832 3855 3878 3902 46 9 11
44 3902 3925 3949 3972 3996 4020 4044 4069 4093 4118 1.4142 || 45° 10 12
45° | 1.4142


(12)
Secant Cosecant
mºmm th
|-#–#–7—& 5 4 3 2 © () nº iñº,
O_1 2 3 4. 5 6–7–5-Fi – 1 2 3 4 5.
1.4142 || 45°
45° | 1.4142 4167 4.192 4217 4242 4267 4293 4318 4344 4370 4396 || 44 || 3 5 810 13
46 4396 4422 44.48 4474 4501 4527 4554 4581 4608 4635 4663 || 43 | 3 5 811 13
47 4663 4690 4718 4746 4774 4802 4830 4859 4887 4916 4945 || 42 || 3 6 8 ll 14
48 4945 4974 5003 5032 5062 5092 5121 5151 5182 5212 5243 || 41 || 3 6 9 12 15
49 5243 5273 5304 5335 5366 5398 5429 5461 5493 5525 1.5557 | 40° l 3 6 9 1316
50° | 1.5557 5590 5622 5655 5688 5721 5755 5788 5822 5856 5890 || 39 || 3 710 1317
51 5890 5925 5959 5994 6029 6064 6099 6135 6171 6207 6243 || 38 || 4 7 11 14 18
52 6243 6279 6316 6353 6390 6427 6464 6502 6540 6578 6616 || 37 || 4 7 11 15 19
53 6616 6655 6694 6733 6772 6812 6852 6892 6932 6972 7013 || 36 || 4 8 12 16 20
54 7013 7054 7095 7137 7179 7221 7263 7305 7348 7391 7434 35 | 4 8 13 1721
55 7434 7478 7522 7566 7610 7655 7700 7745 7791 7837 7883 || 34 || 4 9 13 18:22
56 7883 7929 7976 8023 8070 8118 8166 8214 8263 8312 8361 || 33 || 5 1014 1924
57 8361 8410 8460 8510 8561 8612 8663 8714 8766 8818 8871 || 32 || 510 15 20 26
58 8871 8924 8977 9031 9084 9139 9194 92.49 9304 9360 1.9416 || 31 || 5 11 1622 27
59 | 1.9416 9473 9530 9587 9645 9703 9762 9821 9880 9940ſz.0000 || 30° | 6 12 1823 29
60° | 2.0000 OO61 0122 0183 0245 0308 0371 0434 0498 0562 0627 | 29 61–65
61 0627 0692 0757 0824 0890 0957 1025 1093 1162 1231 1301 || 28 65–70
62 1301 1371. 1441 1513 1584 1657 1730 1803 1877 1952 2027 | 27 70–75
63 2027 2103 2.179 2256 2333 24.12 2490 2570 2650 2,730 28.12 || 26 76–82
64 2812 2894 2976 3060 3144 3228 3314 3400 3486 3574 3662 25 | . 82–88
65 3662 3751 3841 3931 4022 4114 4207 4300 4395 4490 4586 || 24 # 89–96
66 4586 4683 4780 4879 4978 5078 5180 5282 5384 5488 5593 || 23 ||3: 97-105
67 5593 5699 5805 5913. 6022 6131 6.242 6354 6466 6580 6695 || 22 = 106–115
68 6695 6811 6927 7046 7165 7285 7407 7529 7653 7778 7904 || 21 | x 116–126
69 7904 8032 8161 8291 8422 8555 8688 8824 8960 9099 2.9238 20° # 128-139
70° | 2.9238 9379 9521 9665 9811 9957 ſ 0106 0256 0407 0561 3.0716 || 19 |† 141–155
71 || 3.0716 0872 1030 1190 1352 1515 1681 1848 2017 2188 2361 | 18 156–173
72 2361 2535 2712 2891 3072 3255 3440 3628 3817 4009 4203 || 17 174–194
73 4203 4399 4598 4799 5003 5209 5418 5629 5843 6060 6280 | 16 196–220
74 6280 6502 6727 6955 7186 7420 7657 7897 8140 8387 3.8637 || 15 222–250
75 || 3.8637 8890 9147 9408 9672 993.9 ſ 0211 0486 0765 1048 4.1336 || 14
76 || 4.1336 lb27 1923 2223 2527 2837 3150 3469 3792 4121 4454 || 13
77 4454 4.793 5137 5486 5841 6202 6569 6942 7321 7706 4.8097 || 12
78 || 4.8097 8496 8901 9313 97.32 ſ 0159 0593 1034 1484 1942 5.2408 || 11
79 || 5.2408 2883 3367 3860 4362 4874 5396 5928 6470 7023 5.7588 || 10° | Interpolation
80° | 5.7588 8164 8751 9351 9963 ſ os39 1227 1880 2546 3228 6.3925 || 9 | * *
31 | 63925 4637 5366 gill 6874 7655 3454 9273 ſoilz 0572 7.1853 || 3 | **"u"
82 || 7.1853 2757 3684 4635 5611 6613 7642 8700 9787.JO905 8.2055 7
83 || 8.2055 3238 4457 5711 7004 8337 9711ſ 1129 2593 4105 9.5668 6
84 9,567 9,728 9,895 10,068 10,248 10,433 10,626 10,826 11,034 11.249 11,474 5
85 11,474 11.707 11,951 12,204 12,469 12,745 13,035 13,337 13,654 13,987 14,336 4
86 14,336 14,703 15,089 15,496 15,926 16,380 16,862. 17.372 17.914 18,492 19,107 3
87 19,107 19,766 20,471 21,229 22,044 22,926 23,880 24,918 26,050 27,290 28,654 2 InterpOlătiſm
88 28,654 30,161 31.836 33.708 35.815 38,202 40,930 44,077 47,750 52,090 57,299 1 ſlot aſ Gūſát0
89 57,299 63,665 71,622 81,853 95,495 114,59 143,24 190,99 286.48 572,96 oo O9
90° CO


(13)
(FT)
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8Z80 WZ80 Iz80 ZI80 £180 0180 9080 8080 6610 S640 Z610-0 || 0: "I
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SS/O ZSZ0 847/0 Siz/.0 I?/.0 /.2/.0 p.2/0 02/0 9Z/.0 ZZZO 6110 8T"I
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Z890 8/90 +/90 T/90 1990 2990 0990 99.90 ZS90 81790 S4790 9I"I
S$790 Ty30 L.290 2290 0290 9Z90 ZZ90 8T90 SI90 TIQ0 / 090 SI"I
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T2SO LZSO 27SO 6TS0 SISO ZISO 8090 +090 0090 9640 Z6470 ZI"I
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3o-I


1.50
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.60
1.61
1.62
1.63
1.64
1.65
1.66
1.67
1.68
1.69
1.70
1.71
1.72
1.73
1.74
1.75
1.76
1.77
1.78
1.79
1.80
1.81
1.82
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.90
1.91
1.92
1.93
1.94
1.95
1.96
1.97
1.98
1.99
8
0 1 2 3 4 5 6 7 9 10
0.1761 1764. 1767 1770 1772 1775 1778 1781 1784 1787 1790
1790 1793 1796 1798 1801 1804 1807 1810 1813 1816 1818
1818 1821 1824 1827 1830 1833 1836 1838 1841 1844 1847
1847 1850 1853 1855 1858 1861 1864. 1867 1870 1872 1875
1875 1878 1881 1884 1886 1889 1892 1895 1898 1901 1903
1903 1906 1909 1912 1915 1917 1920 1923 1926 1928 1931
1931 1934 1937 1940 1942 1945 1948 1951 1953 1956 1959
1959 1962 1965 1967 1970 1973 1976 1978 1981 1984 1987
1987 1989 1992 1995 1998 2000 2003 2006 2009 2011 2014
2014 2017 2019 2022 2025 2028 2030 2033 2036 2038 2041
0.2041 2044 2047 2049 2052 2055 2057 2060 2063. 2066 2068
2068 2071 2074 2076 2079 2082 2084 2087 2090 2092 2095
2095 2098 2101 2103 2106 2.109 2111. 2114, 21.17 2119 2122
2122 2125 2127 2130 2133 2135 2138 2140 2143 2146 2148
2148 2151 2154 2156 2.159 2162 2164 2167 2170 2172. 2175
2175 2177 2180 2183 2185 2188 2191 2193 2.196 2198 2201
2201 2204 2206 2209 2212 2214 22.17 2219 2222 2225 2227
2227 2230 2232 2235 2238 2240 2243 224.5 2248 2251 2253
2253 2256 2258 2261 2263 2266 2269 2271 2274. 2276 2279
2279 2281 2284 2287 2289 2292 2294 2.297 2299 2302 2304
0.2304 2307 2310 2312 2315 23.17 2320 2.322 2325 2327 2330
2330 2333 2335 2.338 2340 2343 2345 2348 2350 2353 2355
2355 2358 2360 2363 2365 2368 2370 2373 2375 2378 2380
2380 2383 2385 2388 2390 2393 2395 2398 2400 2403 2405
2405 2408 2410 2413 2415 2418 2420 2423 2425 2428 2430
2430 2433 2435 2438 2440 2443 2445 2448 2450 2453 2455
2455 2458 2460 2463 2465 2467 2470 2472 2475 2477 24.80
2480 2482 2485 2487 2490 2492 2494 2497 2499 2502 2504
2504. 2507 2509 2512 2514 2516 2519 2521. 2524 2526 2.529
2529 2531 2533 2536 2538 2541 2543 2545 2.548 2550 2553
0.2553 2555 2558 2560 2562 2565 2567 2570 2572 2574 2577
2577 2579 2582 2584. 2586 2589 2591 2594. 2596 2598 2601
2601 2603 2605 2608 2610 2613 2615 26.17 2620 2622 2625
2625 26.27 2629 2632 2634 2636 2639 2641 2643 2646 2648
2648 2651 2653 2655 2658 2660 2662 2665 2667 2669 2672
2672 2674 2676 2679 2681 2683 2686 2688 2690 2693 2695
2695 2697 2700 2702 2.704, 2707 2709 2711 2.714 2716 2718
2718 2721 2.723 2725 27.28 2730 2732 2735 2737 2739 2742
2742 2744 2746 2749 2751 2753 2755 2758 2760 2762 2765
2765 2767 2769 2772 2.774 2776 2778 2781 2783 2785 2788
0.2788 2790 2792 2794 2797 2799 2801 2804 2806 2808 2810
2810 2813 2815 2817 2819 2822 2824. 2826 2828 2831 2833
2833 2835 2838 2840 2842 2844 2847 2849 2851 2853 2856
2856 2858 2860 2862 2865 2867 2869 2871 2874 2876 2878
2878 2880 2882 2885 2887 2889 2891 2894 2896 2898 2900
2900 2903 2905 2907 2909 2911 2914 2916 2918 2920 2923
2923 2925 2927 2929 2931 2934 2936 2938 2940 2942 2945
2945 2947 2949 2951 2953 2956 2958 2960 2962 2964. 2967
2967 2969 2971. 2973 2975 2978 2980 2982 2984 2986 2.989
2989 2991 2993 2995 2997 2999 3002 3004 3006 3008 3010
* * * * * * * * * * * * * * * * * * * * * * * * * *
flog tan & log ctny


(15)
These two pages give the common logarithms of numbers between 1 and 10, correct to four
places. Moving the decimal point n places to the right (or left) in the number is equivalent
to adding n (or — m) to the logarithm. Thus, log 0.017453 = 0.2419 – 2 [= 2.24191.
For any Angle ac, When a is between 0° and 19.1 When a is between 88°.9 and 90°
log sin a = 2.2419 + log (a:9) | log cos a = 2.2419 + log (90°–39)
... log tan a = 2.2419 + log (tº) log cot a = 2.2419 + log (90°–4%)
2,2419 + log (*) log cot a = 1.7581 – log (*) log tan r = 1.7581—log (90°–3°)
log (ac in radians) =
Log
TÉnths ºf th9
0 1 2 3 4. 5 6 7 8 9 10 || Tallar Diffſellſ
1 2 3 4 5
1.0 l 0.0000 0043 0086 0.128 0170 0212 0253 0294 0334 0374 0414
1.1 0414 0453 0492 O531 0569 0607 0645 0682 0719 0755 0.792
1.2 0792 0828 0864 0899 0934 0969 1004 1038 1072 1106 1139
1.3 1139 1173 1206 1239 1271 1303 1335 1367 1399 1430 1461 || TD AWDid interpſ-
1.4 1461 1492 1523 1553 1584 1614 1644 1673 1703 1732 1761 ||ation in ihò first
1.5 | 1761 1790 1818 1847 1875 1903 1931 1959 1987 2014 2041 | " "." "
16 || 2041 2068 2005 2122 2143 2175 2201 2227 2253 2279 2304 || Sºtº" tº
1.7 || 2304 2330 2355 2330 2405 2430 2455 2430 250A 2529 2553 | * *
1.8 || 2553 2577 2601. 2625 2648 2672 2695 2718 2742 2.765 2788
10° 1.9 || 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 3010
2.0 | 0.3010 3032 3054 3075 3096 3118 3139 3160 3181 3201 3222 8 11
2.1 3222 3243 3263 3284 3304 3324 3345 3365 33.85 3404 3424 8 10
2.2 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 3617 8 10
2.3 3617 3636 3655 3674 3692 371.1 3729 3747 3766 3784 3802
2.4 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 3979
2.5 3979 3997 4014. 4031 4048 4065 4082 4099 4116 4.133 4150
2.6 4150 A166 4183 4200 4216 42.32 4249 4265 4281 4298 4314
2.7 4314. 4330 4346 4362 4378 4393 4409 4425 4440 4456 4472
2.8 4472 4487 4502 4518 4533 45.48 4564 4579 4594 4609 4624
2.9 46.24 4639 4654. 4669 4683 4698 4713 4728 4742 4757 4771
3.0 | 0.4771 4786 4800 4814 4829 4843 4857 4871 4886 4900 4914
3.1 4914 4928 4942 4955 4969 4983 4997 5011 5024 5038 5051
3.2 5051 5065 5079 5092 5105 5119 5132 5145 5159 5172 518.5
3.3 5185 5198 5211 5224 5237 5250 5263 5276 5289 5302 5315
3.4 5315 5328 5340 5353 5366 5378 5391 5403 5416 5428 5441
3.5 5441 5453 5465 5478 5490 5502 5514 5527 5539 5551 5563
3.6 5563 5575 5587 5599 5611. 5623 5635 5647 5658 5670 5682
3.7 5682 5694 5705 5717 5729 5740 5752 5763 5775 5786 5798
3.8 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 5911
3.9 5911 5922 5933 5944 5955 5966 5977 5988 5999 6010 6021
4.0 l 0.6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 6128
4.l 6128 6138 6149 6160 6170 6180 61.91 6201 6212 6222 6232
4.2 6232 6243 6253 6263 6274 6284 6294 6304 6314. 6325 6335
4.3 6335 6345 6355 6365 6375 6385 6395 6405 6415 6425 6435
4.4 6435 6444 6454 6464 6474 6484 6493 6503 6513 6522 6532
4.5 6532 6542 6551 6561 657l 6580 6590 6599 6609 6618 6628
4.6 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 6721
4.7 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 6812
4.8 6812 6821 6830 6839 6848 6857 6866 68.75 6884 6893 6902
4.9 6902 6911 6920 6928 6937 6946 6955 6964 6972 6981 6990
i
log tra 0.4971 log tr/2= 0.1961 log trº= 0.9943 logºv/ºr = 0.2486
log e = 0.4343 (16) log (0.4343) = 1.6378



Log
I– - Tºnths Of th9
0 1 2 3 4. 5 6 7 8 9 10 |Taillar Differentº
- 1 2 3 4 5
5.0 || 0.6990 6998 7007 7016 7024 7033 7042 7050 7059 7067 7076 || 1 2 3 3 4
5.1 7076 7084 7093 7101 7110 7118 7126 7135 7143 7152 7160 || 1 2 3 3 4
5.2 7160 7.168 7177 7185 7193 7202 7210 7218 7226 7235 7243 || 1 2 2 3 4
5.3 || 7243 7251 7259 7267 7275 7284 7292 7300 7308 7316 7324 || 1 2 2 3 4
5.4 7324 7332 7340 7348 7356 7364 7372 7380 7388 7396 7404 || 1 2 2 3 4
5.5 7404 7412 7419 7427 7435 7443 7451 7459 7466 7474 7482 || 1 2 2 3 4
5.6 7482 7490 7497 7505 7513 7520 7528 7536 7543 7551 7559 || 1 2 2 3 4
5.7 7559 7566 7574 7582 7589 7597 7604 7612 7619 7627 7634 || 1 2 2 3 4
5.8 7634 7642 7649 7657 7664 7672 7679 7686 7694 7701 7709 || 1 1 2 3 4
5.9 7709 7716 7723 7731 7738 7745 7752 7760 7767 7774 7782 l l 2 3 4
6.0 || 0.7782 7789 7796 7803 7810 7818 7825 7832 7839 7846 7853 || 1 1 2 3 4
6.1 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 7924 || 1 1 2 3 4
6.2 7924 7931 7938 7945 7952 7959 7966 7973 7980 7987 7993 || 1 1 2 3 3
6.3 7993 8000 8007 8014 8021 8028 8035 8041 8048 8055 8062 || 1 1 2 3 3
6.4 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 8129 || 1 1 2 3 3
6.5 8129 8136 8142 8149 8156 8162 8169 8176 8182 8189 8195 || 1 1 2 3 3
6.6 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 8261 || 1 1 2 3 3
6.7. 8261 8267 8274 8280 8287 8293 8299 8306 8312 8319 8325 || 1 1 2 3 3
6.8 8325 8331 8338 8344 8351 8357 8363 8370 8376 8382 8388 || 1 1 2 3 3
6.9 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 8451 || 1 1 2 3 3
7.0 || 0.8451 8457 8463 3470 8476 8482 8488 8494 8500 8506 8513 || 1 1 2 2 3
7.1 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 8573 || 1 1 2 2 3
7.2 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 8633 || 1 1 2 2 3
7.3 8633 8639 8645 8651 8657 8663 8669 8675 8681 8686 8692 || 1 1 2 2 3
7.4 8692 8698 8704 8710 8716 87.22 8727 8733 8739 8745 8751 || 1 1 2 2 3
7.5 8751 8756 8762 8768 87.74 8779 8785 8791 8797 8802 8808 || 1 1 2 2 3
7.6 8808 8814 8820 8825 8831 8837 8842 8848 8854 8859 8865 || 1 1 2 2 3
7.7 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 8921 || 1 1 2 2 3
7.8 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 8976 || 1 1 2 2 3
7.9 8976 8982 8987 8993 8998 9004 9009 9015 9020 9025 9031 || 1 1 2 2 3
8.0 || 0.9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 9085 || 1 1 2 2 3
8.l. 9085 9090 9096 9101 9106 9112 9117 9122 9128 9133 9138 || 1 1 2 2 3
8.2 9138 9143 9149 91.54 9159 9165 9170 9175 9180 9186 9191 || 1 1 2 2 3
8.3 9191 9.196 9201 9206 92.12 92.17 9222 9227 9232 9238 9243 || 1 1 2 2 3
8.4 9243 9248 9253 9258 9263 9269 9274 92.79 9284 9289 92.94 || 1 1 2 2 3
8.5 9294 9299 9304 9309 9315 932O 9325 9330 9335 9340 9345 || 1 1 2 2 3
8.6 || 9345 9350 9355 9360 9365 9370 93.75 9380 9385 9390 9395 || 1 1 2 2 3
8.7 9395 9400 9405 9410 94.15 9420 9425 9430 9435 94.40 9445 || 0 1 1 2 2
8.8 9445 9450 94.55 9460 94.65 9469 9474 94.79 9484 9489 94.94 || 0 1 1 2 2
8.9 9494. 9499 95.04 9509 9513 9518 9523 9528 9533 95.38 9542 || 0 1 1 2 2
9.0 || 0.9542 9547 9552 95.57 9562 9566 95.71 9576 9581 9586 9590 || 0 1 1 2 2
9.1 9590 9595 9600 9605 9609 9614 96.19 9624 9628 9633 9638 || 0 1 1 2 2
9.2 9638 9643 9647 9652 9657 9661 9666 9671 96.75 9680 9685 || 0 1 1 2 2
9.3 || 9685 96.89 9694 9699 97.03 9708 9713 97.17 9722 97.27 97.31 || 0 1 1 2 2
9.4 97.31 97.36 9741 9745 9750 9754. 9759 9763 9768 9773 97.77 || 0 1 1 2 2
9.5 97.77 9782 9786 9791 97.95 9800 9805 9809 9814 98.18 98.23 : 0 1 1 2 2
9.6 9823 9827 9832 9836 98.41 9845 9850 9854 9859 9863 9868 || 0 1 1 2 2
9.7 9868 98.72 9877 9881 9886 9890 98.94 9899 9903 9908 9912 || 0 1 1 2 2
9.8 99.12 99.17 992.1 9926 9930 99.34 9939 9943 9948 9952 9956 || 0 1 1 2 2
9.9 9956 996.1 9965 9969 9974 9978 9983 9987 9991 9996 0 1 1 2 2
(17)



flog tan & logctnº
* Ł9.G...........I.T PT
Log Sin - Log Cos
-ā-ā–4–4–5 4 3 2 1 0)
0 1 2 3 4 5 6 7-5-5-1
0°.0 || -oo 4.2419 5429 7190 8439 9408 ſ 0200 0870 1450 1961 3.2419 | 89.9
0.1 ! 3.2419 2833 3211 3558 3880 4180 4460 4723 4971 5206 5429 | 89.8
0.2 5429 5641 5843 6036 6221 6398 6568 6732 6890 7043 7190 | 89.7
0.3 7190 7332 7470 7604 7734 7859 7982 8101 8217 8329 8439 || 89.6
0.4 8439 8547 8651 8753 8853 8951 9046 9140 9231 9321 3.9408 | 89.5
0.5 || 3.9408 9494. 9579 9661 9743 9822 9901 9977 ſoos3 0127 2.0200 | 89.4
0.6 || 2.0200 0272 0343 0412 0480 0548 0614 0679 0744 0807 0870 | 89.3
0.7 0870 0931 0992 1052 1111 1169 1227 1284 1340 1395 1450 | 89.2
0.8 1450 1503 1557 1609 1661 1713 1764. 1814 1863 1912 1961 | 89.1
0.9 1961 2009 2056 2103 2150 2196. 2241 2286 2331 2375 2.2419 |39°.0
1°.0 2.2419 2462 2505 2547 2589 2630 2672 2712 2753 2793 2832 || 88.9
1.1 2832 2872 2911 2949 2988 3025 3063 3100 3137 3174 3210 || 88.8
1.2 3210 3246 3282 3317 3353 3388 3422 3456 3491 3524 3558 || 88.7
1.3 3558 3591 3624 3657 3689 3722 3754 3786 3817 3848 3880 || 88.6
1.4 3880 3911 3941 3972 4002 4032 4062 4091 4121 4150 Al'79 88.5
1.5 4179 4208 4237 4265 4293 4322 4349 4377 4405 4432 4459 || 88.4
1.6 4459 4486 4513 4540 4567 4593 4619 4645 4671 4697 4723 || 88.3
1.7 4723 4748 4773 4799 4824. 4848 4873 4898 4922 4947 4971 || 88.2
1.8 4971 4995 5019 5043 5066 5090 5113 5.136 5160 5183 5206 || 88.1
1.9 5206 5228 5251 5274 5296 5318 5340 5363 5385 5406 2.5428 |33°.O.
2°.0 | 2.5428 5450 5471 5493 5514 5535 5557 5578 5598 5619 5640 || 87.9
2.1 5640 5661 5681 5702 5722 5742 5762 5782 5802 5822 5842 || 87.8
2.2 5842 5862 5881 5901 5920 5939 5959 5978 5997 6016 6035 | 87.7
2.3 6035 6054 6072 6091 6110 6128 6147 6.165 6183 6201 6220 || 87.6
2.4 6220 6238 6256 6274 6291 6309 6327 6344 6362 6379 6397 || 87.5
2.5 6397 6414 6431 6449 6466 6483 6500 65.17 65.34 6550 6567 || 87.4
2.6 6567 6584 6600 6617 6633 6650 6666 6682 6699 6715 6731 || 87.3
2.7 6731 6747 6763 6779 6795 6810 6826 6842 6858 6873 6889 || 87.2
2.8 6889 6904 6920 6935 6950 6965 6981 6996 7011 7026 7041 || 87.1
2.9 7041 7056 7071 7086 7100 7115 7130 7144 7159 7174 2.7188 #37°.0
3°.0 || 2.7188 7202 7217 7231 7245 7260 7274 7288 7302 7316 7330 || 86.9
3.1 7330 7344. 7358 7372 7386 7400 7413 7427 74.41 7454 7468 || 86.8
3.2 7468 7482 7495 7508 7522 7535 7549 7.562 7575 7588 7602 || 86.7
3.3 7602 7615 7628 7641 7654 7667 7680 7693 7.705 7718 7731 || 86.6
3.4 7731 7744 7756 7769 7782 7794 7807 7819 7832 7844. 7857 || 86.5
3.5 7857 7869 7881 7894 7906 7918 7930 7943 7955 7967 7979 || 86.4
3.6 7979 7991 8003 8015 8027 8039 8051 8062 8074 8086 8098 || 86.3
3.7 8098 8109 8121 8133 8144 8156 8168 8179 8191 8202 8213 || 86.2
3.8 8213 8225 8236 8248 8259 8270 8281 82.93 8304 83.15 8326 || 86.1
3.9 || 8326 8337 8348 8359 8370 8381 8392 8403 8414 8425 2.8436 |36°.0
4°.0 | 2.8436 8447 8457 8468 8479 8490 8500 8511 8522 8532 8543 || 85.9
4.l 8543 8553 8564 8575 8585 8595 8606 8616 8627 8637 8647 || 85.8
4.2 8647 8658 8668 8678 8688 8699 8709 8719 8729 8739 8749 || 85.7
4.3 8749 8759 8769 8780 8790 8799 8809 8819 8829 8839 8849 85.6
4.4 8849 8859 8869 8878 8883 3898 8908 8917 3927 8937 8946 i 85.5
4.5 8946 8956 8966 8975 8985 8994. 9004 9013 9023 9032 9042 || 85.4
4.6 9042 9051 9060 9070 9079 9089 9098 9107 9116 91.26 9135 | 85.3
4.7 91.35 9144 91.53 9162 9172 9181 91.90 91.99 92.08 92.17 92.26 || 85.2
4.8 9226 9235 9244 9253 9262 9271 92.80 9289 92.98 9307 9315 || 85.1
4.9 9315 9324 9333 9342 9351 9359 9368 9377 9386 9394 2.9403 ||35°.()
(18)
Tºnths ºf th9
Taillaſ Diff}ſBI|| 0
1 2 3 4 5
TD AWDid interp0-
|ātūſ in th9 first
Blººm linBS, USB
IOtB in the tabl6 Of
|Ogårithms Of ſlum-
|BIS,
(Ordinary inter-
DOlation WOuld ſiſt
56 aſ Qūſātū in th9
first thr60 linéS,)
8 11 15 19
7 10 14 17
6 10 13 16
6 9 12 15
8 ll 14
8 11 13
7 10 12
9 12
9 ll
8 11
8 10
8 lo


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|0
|0
\ L O G
Log Sin Log Cos
|-e & . - -
0. 7 .5 4. 3 2 ..] ()
& 1 e .5 6T-ā-ā-
– oo | 90°
0° | – c. 3.2419 5429 7190 8439 9408 ſ 0200 0870 1450 1961 2.2419 | 89
1 || 2.2419 2832 3210 3558 3880 4179 4459 4723 4971 5206 5428 | 88
2 5428 5640 5842 6035 6220 6397 6567 6731 6889 7041 7188 || 87
3 7188 7330 7468 7602 7731 7857 7979 8098 8213 8326 8436 || 86
4 8436 8543 8647 8749 8849 8946 9042 9135 9226 9315 2.9403 | 85
5 || 2.9403 9489 9573 9655 9736 9816 9894 9970ſo046 0120 I.0192 | 84
6 || I.0192 0264 0334 0403 0472 0539 0605 0670 0734 0797 0859 || 83
7 0859 0920 0981 1040 1099 1157 1214 1271 1326 1381. 1436 || 82
8 1436 1489 1542 1594 1646 1697 1747 1797 1847 1895 1943 || 81
9 1943 1991 2038 2085 2131 2176 2221 2266 2310 2353 T.2397 | 80°
10° | T.2397 2439 2482 2524 2565 2606 2647 2687 2727 2767 2806 || 79
11 2806 2845 2883 2921 2959 2997 3034 3070 3107 3143 3179 || 78
12 3179 3214 3250 3284 3319 3353 3387 3421 3455 3488 3521 || 77
13 3521 3554 3586 3618 3650 3682 3713 3745 3775 3806 3837 || 76
14 3837 3867 3897 3927 3957 3986 4015 4044 40.73 4102 4130 || 75
15 4130 41.58 4186 4214 4242 4269 4296 4323 4350 4377 4403 || 74
16 4403 4430 4456 4482 4508 4533 4559 4584 4609 4634. 4659 || 73
17 4659 4684 4709 4733 4757 4781 4805 4829 4853 4876 4900 || 72
18 4900 4923 4946 4969 4992 5015 5037 5060 5082 5104 5126 || 71
19 5126 5148 5170 5192 5213 5235 5256 5278 5299 5320 T.5341 || 70°
20° | 1.5341 5361 5382 5402 5423 5443 5463 5484 5504 5523 5543 | 69
21 5543 5563 55.83 5602 5621 5641 5660 5679 5698 5717 5736 | 68
22 5736 5754 5773 5792 5810 5828 5847 5.865 5883 5901 5919 || 67
23 5919 5937 5954 5972 5990 6007 6024 6042 6059 6076 6093 || 66
24 6093 6110 6127 6144 6161 6177 61.94 6210 6227 6243 6259 || 65
25 6259 62.76 6292 6308 6324 6340 6356 6371 6387 6403 6418 || 64
26 6418 6434 6449 6465 6480 6495 6510 6526 6541 6556 65.70 || 63
27 6570 6585 6600 6615 6629 6644 6659 6673 6687 6702 6716 || 62
28 6716 6730 6744 6759 6773 6787 6801 6814 6828 6842 6856 || 61
29 6856 6869 6883 6896 6910 6923 6937 6950 6963 6977 I.6990 || 60°
30° | T.6990 7003 7016 7029 7042 7055 7068 7080 7093 7106 7118 || 59
31 7118 7131 7144. 7156 7.168 7181 7.193 7205 7218 7230 7242 || 58
32 7242 7254. 7266 7278 7290 7302 7314 7326 7.338 7349 7361 57
33 7361 7373 7384 7396 7407 7419 7430 7442 7453 7464 7476 56
34 7476 7487 7498 7509 7.520 7531 7542 7553 7564 7575 7586 55
35 7586 7597 7607 7618 7629 7640 7650 7661 7671 7682 7692 || 54
36 7692 7703 7713 7723 7734 7744 7754 7764 7774 7785 7795 53
37 7795 7805 7815 7825 7835 7844. 7854 7864 7874 7884 7893 || 52
38 7893 7903 7913 7922 7932 7941 7951 7960 7970 7979 7989 || 51
39 7989 7998 8007 8017 8026 8035 8044 8053 8063 8072 I.8081 || 50°
40° l T.8081 8090 8099 8108 8117 8125 8134 8143 8152 8161 8169 49
41 8169 8178 8.187 8195 8204 8213 8221 8230 8238 8247 8255 || 48
42 8255 8264 8272 8280 8289 8297 8305 8313 8322 8330 8338 || 47
43 8338 8346 8354 8362 8370 8378 8386 8394 8402 8410 84.18 || 46
44 8418 8426 8433 8441 8449 8457 8464 8472 8480 8487 T.8495 || 45°
45° | T.8495
TBnths 0f the
Tabulaſ DifferBſ108
1 2 3 4 5
T0 aWDid interp0-
lation in the first
têſ lim8S, USB th9
Sp8Gial tabl60ſ th9
DIBCBſſing pågø.
(Ordinary inter-
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8 12 16 20
7 11 15 19
7 10 14 17
9 13 16
9 12 15
8 11 14
8 10 13
7 10 12
9 11
9 ll
8 10
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(20)
Log Sin Log Cos
º © H Tônths Of th
0 H Ž à ă # # ; # + () º
83 9968 9968 9969 99.70 9971 99.72 9973 99.74 99.75 99.75 9976
84 9976 9977 99.78 99.78 9979 9980 9981 9981 9982 9983 9983
85 9983 9984 9985 9985 9986 9987 99.87 9988 9988 99.89 99.89
86 9989 9990 9990 99.91 9991 9992 9992 9993 9993 9994. 9994
87 9994. 9994. 9995 9995 9996 9996 9996 9996 9997 9997 9997
88 9997 9998 9998 9998 9998 9999 9999 9999 9999 9999 I.9999
89 I.9999 9999.ſ0000 0000 0000 0000 0000 0000 0000 0000 0.0000
90° 0.0000
O
9 1 2 3 4 5
T.8495 || 45°
45° T.8495 8502 8510 8517 8525 8532 8540 8547 8555 8562 8569 || 44 || 1 1 2 3 4
46 8569 8577 8584 8591 8598 8606 8613 8620 8627 8634 8641 || 43 || 1 1 2 3 4
47 8641 8648 8655 8662 8669 8676 8683 8690 8697 8704 87ll || 42 || 1 1 2 3 3
48 8711 8718 8724 8731 8738 8745 8751 8758 8765 8771 8778 || 41 || 1 1 2 3 3
49 8778 8784 8791 8797 8804 8810 8817 8823 8830 8836 T.8843 | 40° | 1 1 2 3 3
50° | T.8843 8849 8855 8862 8868 8874 8880 8887 8893 8899 8905 || 39 || 1 1 2 2 3
51 8905 8911 8917 8923 8929 8935 8941 8947 8953 8959 8965 || 38 || 1 1 2 2 3
52 8965 8971 8977 8983 8989 8995 9000 9006 9012 9018 9023 || 37 || 1 1 2 2 3
53 9023 9029 9035 9041 9046 9052 9057 9063 9069 9074 9080 || 36 || 1 1 2 2 3
54 9080 9085 9091 9096 9101 9107 9112 9118 9123 9128 9134 || 35 | 1 1 2 2 3
55 9134 9139 9144 9149 9155 9160 9165 9170 91.75 9181 9186 || 34 || 1 1 2 2 3
56 9186 9191 91.96 9201 9206 92.11 92.16 9221 9226 9231 9236 || 33 || 1 1 2 2 3
57 9236 9241 9246 9251 92.55 9260 9265 92.70 9275 92.79 9284 || 32 || 0 1 1 2 2
58 9284 9289 92.94 9298 9303 9308 9312 9317 9322 9326 9331 || 31 || 0 1 1 2 2
59 9331 9335 9340 9344 9349 9353 9358 9362 9367 9371 T.9375 || 30° | 0 1 1 2 2
60° | T.9375 9380 9384 9388 93.93 9397 9401 9406 9410 9414 9418 || 29 || 0 1 1 2 2
61 9418 9422 9427 9431. 9435 9439 9443 9447 9451 94.55 9459 || 28 || 0 1 1 2 2
62 9459 94.63 9467 94.71 94.75 94.79 94.83 9487 9491 9495 9499 || 27 || 0 l l 2 2
63 9499 95.03 9506 95.10 9514 9518 9522 9525 95.29 9533 9537 || 26 || 0 1 1 2 2
64 9537 9540 9544 9548 9551 9555 9558 9562 9566 9569 9573 || 25 || 0 l l l 2
65 9573 9576 9580 95.83 9587 9590 9594 95.97 9601 9604 9607 || 24 || 0 1 1 1 2
66 9607 96ll 9614 96.17 9621 9624 9627 9631 9634 9637 9640 || 23 || 0 l l l 2
67 9640 9643 9647 9650 9653 9656 9659 9662 9666 9669 9672 || 22 || 0 l l l 2
68 9672 96.75 9678 9681 9684 9687 9690 9693 9696 9699 9702 || 21 || 0 1 l l 1
69 9702 9704 9707 9710 9713 97.16 9719 9722 9724 9727 I.9730 20° 0 1 1 1 1
70° | T.973O 9733 9735 9738 9741 9743 9746 9749 9751 9754 9757 | 19 || 0 1 1 1 1
71 97.57 97.59 9762 9764 9767 9770 9772 9775 97.77 9780 9782 | 18 || 0 1 1 1 1
72 9782 9785 9787 9789 9792 97.94 9797 9799 9801 9804 9806 || 17 || 0 0 1 1 1
73 9806 98.08 9811 98.13 9815 98.17 9820 9822 9824 9826 98.28 || 16 || 0 0 1 1 1
74 98.28 98.31 9833 9835 9837 9839 98.41 98.43 9845 9847 9849 || 15 || 0 0 1 1 1
75 9849 9851 9853 98.55 98.57 9859 9861 9863 9865 9867 98.69 || 14 || 0 0 1 1 1
76 98.69 98.71 98.73 9875 9876 98.78 9880 9882 9884 9885 98.87 || 13 || 0 0 1 1 1
77 9887 9889 9891 9892 98.94 9896 9897 9899 9901 9902 9904 || 12 || 0 0 1 1 1
78 9904 9906 9907 9909 9910 9912 9913 9915 9916 9918 9919 || 11 || 0 0 0 1 1
79 9919 9921 9922 9924 9925 9927 9928 9929 9931 9932 T.9934 || 10° || 0 0 0 1 1
80° | T.9934 9935 9936 9937 9939 99.40 9941 9943 9944 9945 9946 9 || 0 0 0 1 1
81 9946 994.7 99.49 9950 9951 9952 99.53 9954 9955 9956 9958 0 0 0 0 1
82 9958 9959 9960 996.1 9962 9963 9964 9965 9966 9967 9968 0 0 0 O 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
(21)


#log tan & log ctnº
"…~!1.9 G .............. *. log sin a ſoq cos /
Log Tan Log Coſtam
|-º-º-Z–6 5 4 3 | ()
0 1 2 3 4 5 6 7 T3 9T
0°.0 || – o 4.2419 5429 7190 8439 9408 ſ 0200 0870 1450 1961 3.2419 || 89.9
0.1 ! 3.2419 2833 3211 3558 3880 4180 4460 4723 4972 5206 5429 | 89.8
0.2 5429 5641 5843 6036 6221 6398 6569 6732 6890 7043 7190 | 89.7
0.3 7190 7332 7470 7604. 7734 7860 7982 8101 8217 83.29 8439 || 89.6
0.4 8439 8547 8651 8754 8853 8951 9046 9140 9231 9321 3.9409 | 89.5
0.5 || 3.9409 9495 9579 9662 9743 9823 9901 9978 ſooš3 0127 2,0200 | 89.4
0.6 | 2.0200 0272 0343 0412 0481 0548 0614 0680 0744 0807 0870 | 89.3
0.7 O870 0932 0992 1052 1111 1170 1227 1284 1340 1395 1450 | 89.2
0.8 1450 1504 1557 1610 1662. 1713 1764. 1814 1864. 1913 1962 | 89.1
0.9 1962 2010 2057 2104 2150 2196. 2242 2287 2331 2376 2.2419 |39°.0i
1°.0 | 2.2419 2462 2505 2548 2590 2631 2672 2713 2754 2794 2833 || 88.9
1.1 2833 2873 2912 2950 2988 3026 3064. 3101 3138 3175 3211 i 88.8
1.2 3211 3247 3283 3318 3354 3389 3423 3458 3492 3525 3559 || 88.7
1.3 3559 3592 3625 3658 3691 3723 3755 3787 3818 3850 3881 || 88.6
1.4 3881 3912 3943 3973 4003 4033 4063 4093 4122 4152 4181 || 88.5
1.5 4181 4210 4238 4267 4295 4323 4351 4379 4406 4434 4461 || 88.4
1.6 4461 4488 4515 4542 4568 4595 462.l. 4647 4673 4699 4725 || 88.3
1.7 4725 4750 4775 4801 4826 4851 4875 4900 4924. 4949 4973 || 88.2
l.8 4973 4997 5021 5045 5068 5092 5115 5139 5162 518.5 5208 || 88.1
1.9 5208 5231 5253 5276 5298 5321 5343 5365 5387 5409 2.5431 38°.0]
2°.0 | 2.5431 5453 5474 5496 5517 5538 5559 5580 5601 5622 5643 | 87.9
2.1 5643 5664 5684 5705 5725 5745 5765 5785 5805 5825 5845 || 87.8
2.2 5845 5.865 5884 5904 5923 5943 5962 5981 6000 6019 6038 || 87.7
2.3 6038 6057 6076 6095 6113 6132 6150 6169 6.187 6205 6223 || 87.6
2.4 6223 6242 6260 6277 6295 6313 6331 6348 6366 6384 6401 || 87.5
2.5 6401 6418 6436 6453 6470 6487 6504 6521 6538 6555 6571 i 87.4
2.6 6571 6588 6605 6621 6638 6654 6671 6687 6703 6719 6736 || 87.3
2.7 6736 6752 6768 6784 6800 6815 6831 6847 6863 6878 6894 || 87.2
2.8 6894 6909 6925 6940 6956 6971 6986 7001 7016 7031 7046 87.1
2.9 7046 7061 7076 7091 7106 7121 7136 7150 7165 7179 2.7194 (37°.0
3°.0 || 2.7194 7208 7223 7237 7252 7266 7280 7294 7308 7323 7337 || 86.9
3.1 7337 7351 7365 7379 7392 7406 7420 7434 7448 7461 7475 || 86.8
3.2 7475 7488 7502 75.15 7529 75.42 7556 7569 7582 7596 7609 || 86.7
3.3 7609 7622 7635 7648 7661 7674 7687 7700 7713 77.26 7739 86.6
3.4 7739 7751 7764 7777 7790 7802 7815 7827 7840 7852 7865 || 86.5
3.5 7865 7877 7890 7902 7914 7927 7939 7951 7963 7975 7988 || 86.4
3.6 7988 8000 8012 8024 8036 8048 8059 8071 8083 8095 8107 || 86.3
3.7 8107 8119 8130 8142 8154 8165 8.177 8188 8200 8212 $223 || 86.2
3.8 8223 8234 8.246 8257 8269 8280 8291 8302 8314 8325 8336 || 86.1
3.9 8336 8347 8358 8370 8381 8392 8403 8414 8425 8436 2.8446 26°C
4°.0 | 2.8446 8457 8468 8479 8490 8501 8511 8522 8533 8543 8554 | 85.9
4.1 8554 85.65 8575 8586 8596 8607 8617 8628 86.38 8649 8659 || 85.8
4.2 8659 8669 8680 8690 8700 8711. 8721 8731 8741 8751 8762 || 85.7
4.3 8762 87.72 8782 8792 8802 8812 8822 8832 8842 8852, 8862 || 85.6
4.4 8862 8872 8882 8891 8901 8911. 8921 8931. 8940 8950 8960 || 85.5
4.5 8960 8970 8979 8989 8998 9008 9018 9027 9037 9046 9056 || 85.4
4.6 9056 9065 90.75 9084 9093 9103 9112 9122 9131 91.40 9150 || 85.3
4.7 91.50 9159 9168 91.77 9186 91.96 9205 9214 9223 9232 9241 || 85.2
4.8 9241 9250 9260 9269 92.78 92.87 9296 9305 9313 9322 9331 || 85.1
4.9 9331 9340 9349 9358 9367 93.76 9384 9393 9402 9411 2.9420 |35°.()
(22)
Tºnths 0f th9
Tabular Differenſ}
1 2 3 4 5
TO AV0id interp0-
latſ0n in the first
8|BVBſ ſin&S, USB
|Otſ in th9 tablº Of
10garithms Of ſlum-
|BIS,
(Ordinary intër-
pOlătiſſ WOuld not
b6 3CCIIſātā iſ th9
first thrBB linéS.)
8 11 15 19
7 10 14 17
6 10 13 16
6 9 12 15
8 11 14
8 11 13
7 10 12
9 12
9 11
8 11
8 10
8 10
:i.::::
\


Log
Tan
º-º-º-º-
Log Coſtam
L 9 & 7 (6 5 4. 3 2 | ()
- º 0 1 2 3TT5-ā-ā–#——
5°.0 | 2.9420 9428 9437 9446 9454 9463 9472 94.80 9489 9497 2.9506 | 84.9
5.1 9506 9515 9523 9532 9540 9549 95.57 9565 95.74 9582 9591 | 84.8
5.2 95.91 9599 9608 96.16 96.24 9633 9641 9649 9657 9666 9674 | 84.7
5.3 9674 9682 9690 9699 97.07 9715 9723 97.31 97.39 97.47 9756 | 84.6
5.4 9756 9764 9772 9780 9788 9796 9804 9812 9820 9828 9836 | 84.5
5.5 9836 9844. 9852 9860 9867 9875 9883 9891 98.99 9907 9915 | 84.4
5.6 9915 9922 9930 9938 9946 9953 99.61 9969 9977 9984 2.9992 | 84.3
5.7 || 2.9992 ſ 0000 0007 0015 0022 0030 0038 0045 0053 0060 I.0068 || 84.2
5.8 || I.0068 0075 0083 0090 0098 0105 O113 0120 0128 0.135 0.143 | 84.1
5.9 0.143 0150 0157 0.165 0172 0180 0187 0194 0202 0209 I.0216 |34°.0
6°.0 | I.0216 0223 0231 0238 0245 0253 0260 0267 0274 0281 0289 || 83.9
6.1 0289 0296 0303 0310 0317 0324 0331 0338 0346 0353 0360 | 83.8
6.2 0360 0367 0374 0381 0388 0395 0402 0409 0416 0423 0430 83.7
6.3 0430 0437 0444 04:51 0457 0464 0471 0478 0485 0492 0499 || 83.6
6.4 0499 0506 0512 0519 0526 0533 0540 0546 0553 0560 0567 83.5
6.5 0567 0573 0580 0587 0593 0600 0607 0614 0620 0627 0633 || 83.4
6.6 0633 0640 0647 0653 0660 0667 0673 0680 0686 0693 0699 || 83.3
6.7 O699 0706 0712 0719 0725 0732 0738 0745 0751 0758 0.764 || 83.2
6.8 0764 0771 0777 0784 0790 0796 0803 0809 0816 0822 0828 || 83.1
6.9 || 0828 0835 0841 0847 0854 0860 0866 0873 0879 0885 I.0891 (33°.0
7°.0 | I.0891 0898 0904 0910 0916 0923 0929 0935 0941 0947 0954 | 82.9
7.1 0954 0960 0966 0972 0978 0.984 0991 0997 1003 1009 1015 || 82.8
7.2 1015 1021 1027 1033 1039 1045 1051 1058 1064 1070 1076 || 82.7
7.3 1076 1082 1088 1094. 1100 1106 1112 1117 1123 1129 1135 | 82.6
7.4 1135 1141 1147 1153 1159 1165 1171 1177 1183 1188 1194 || 82.5
7.5 1194 1200 1206 1212 1218 1223 1229 1235 1241 1247 1252 || 82.4
7.6 1252 1258 1264. 1270 1276 1231 1287 1293 1299 1304 1310 || 82.3
7.7 1310 1316 1321 1327 1333 1338 1344 1350 1355 1361 1367 | 82.2
7.8 1367 1372 1378 1384 1389 1395 1400 1406 1412 1417 1423 82.1
7.9 1423 1428 1434 1439 1445 1450 1456 1461 1467 1473 I.1478 |32°.0
8°.0 l I.1478 1484 1489 1494 1500 1505 1511 1516 1522 1527 1533 | 81.9
8.1 1533 1538 1544 1549 1554 1560 1565 1571 1576. 1581 1587 || 81.8
8.2 1587 1592 1597 1603 1608 1613 1619 1624 1629 1635 1640 | 81.7
8.3 1640 1645 1651 1656 1661 1667 1672 1677 1632 1688 1693 || 81.6
8.4 1693 1698 1703 1709 1714 1719 1724. 1729 1735 1740 1745 || 81.5
8.5 1745 1750 1755 1761 1766 1771 1776 1781 1786 1791 1797 || 81.4
8.6 1797 1802 1807 1812 1817 1822 1827 1832 1837 1842 1848 || 81.3
8.7 1848 1853 1858 1863 1868 1873 1878 1883 1888 1893 1898 || 81.2
8.8 1898 1903 1908 1913 1918 1923 1928 1933 1938 1943 1948 || 81.1
8.9 1948 1953 1958 1963 1968 1973 1977 1982 1987 1992 T.1997 131°.()
9°.0 | I.1997 2002 2007 2012 2017 2022 2026 2031 2036 2041 2046 || 80.9
9.1 2046 2051 2056 2060 2065. 2070 2075 2080 2085 2089 2094 || 80.8
9.2 2094. 2099 2104 2109 2113 2118 2123 2128 2132 2137 2142 80.7
9.3 2142 2147 2151 2156 2161 2166 2170 2175 2180 2185 2189 || 80.6
9.4 2189 2.194. 2199 2203 2208 2213 22.17 2222 2227 2231 2236 || 80.5
9.5 2236 2241 224.5 2250 2255 2259 2264 2269 2273 2278 2282 || 80.4
9.6 2282 2287 2292 2296 2301 2305 2310 2315 2319 2324 2328 || 80.3
9.7 2328 2333 2337 2342 2346 2351 2356 2360 2365 2369 2374 || 80.2
9.8 2374 2378 2383 2387 2392 2396 2401 2405 2410 2414 - 2419 || 80.1
9.9 | 1.2419 2423 2428 2432 2437 2441 2445 2450 2454 2459 T.2463 30° (O)
(23)
1
Tºnths Of th9
Tabular DifferBm08
2
3
4.
5


_m - logtanalog ctn\
L O G A $. log sin a ſog cos A
Log Tan Log Coſtam
|-º-º-'7 & | Tenths ºf the
0 1 #- (§ 5 # 3 2 © Q Tabular DiffºrtſC8
== .1 2 3 4. TET -i-º-º:- 1 2 3 4 5
- Co 90°
0° | – Co 3.2419 5429 7190 8439 9409 ſ 0200 0870 1450 1962 2.2419 | 89 TO AV0id intërD0-
1 || 2.2419 2833 3211 3559 3881 4181 4461 4725 4973 5208 5431 || 88 lation i. th9 º
2 5431 5643 5845 6038 6223 6401 657l 6736 6894 7046 7.194 || 87 tBſ linôS LS6 th9
3 7194 7337 7475 7609 7739 7865 7988 8107 8223 8336 – 8446 86 Sp8Gial tablº Oſ th9
4 8446 8554 8659 8762 8862 8960 9056 9150 924l 9331 2.9420 || 85 pſ303ding pågø.
5 || 2.9420 9506 9591 9674 9756 9836 9915 9992 ſoo;8 0.143 I.0216 | 84 (Ordinary inter-
6 || 1.0216 0289 0360 0430 0499 0567 0633 0699 0764 0828 0891 || 83 | polation WOuld not
7 0891 0954 1015 1076 1135 1194 1252 1310 1367 1423 1478 || 82 | |0 aſ Cuſatº in th9
8 1478 1533 1587 1640 1693 1745 1797 1848 1898 1948 1997 || 81 | first thré6 ſilëS.)
9 1997 2046 2094 2142 2189 2236 2282 2328 2374. 2419 I.2463 || 30°
10° | T.2463 2507 2551 2594 2637 2680 2722 2764 2805 2846 2887 || 79 || 4 8 13 1721
ll 2887 2927 2967 3006 3046 3085 3123 3162 3200 3237 3275 || 78 || 4 8 12 16 19
12 3275 3312 3349 3385 3422 3458 3493 3529 3564 3599 3634 || 77 || 4 7 11 14 18
13 3634 3668 3702 3736 377.0 3804 3837 3870 3903 3935 3968 || 76 || 3 7 10 13 17
14 3968 4000 4032 4064 4095 4127 4.158 4189 4220 4250 4281 || 75 || 3 6 9 13 16
15 4281 4311 4341. 4371 4400 4430 4459 4488 4517 4546 4575 || 74 || 3 6 9 12 15
16 45.75 4603 4632 4660 4688 4716 4744 4771 4799 4826 4853 || 73 || 3 6 8 ll 14
17 4853 4880 4907 4934 4961 4987 5014 5040 5066 5092 5118 || 72 || 3 5 8 ll 13
18 5118 51.43 5169 5195 5220 5245 5270 5295 5320 5345 53.70 || 71 || 3 5 8 10 13
19 5370 5394 5419 5443 5467 5491 5516 5539 5563 5587 I.56ll || 70° || 2 5 7 10 12
20° | I.5611 5634 5658 5681 5704 5727 5750 5773 5796 5819 5842 | 69 || 2 5 7 10 12
21 5842 5864 5887 5909 5932 5954 5976 5998 6020 6042 6064 | 68 || 2 4 7 9 11
22 6064 6086 6108 6129 6151 6172 61.94 6215 6236 6257 6279 || 67 || 2 4 6 9 ll
23 6279 6300 6321 6341 6362 6383 6404 6424 6445 6465 6486 || 66 || 2 4 6 8 10
24 6486 6506 6527 6547 6567 6587 6607 6627 6647 6667 6687 || 65 || 2 4 6 8 10
25 6687 6706 6726 6746 6765 6785 6804 6824 6843 6863 6882 || 64 || 2 4 6 8 10
26 6882 6901 6920 6939 6958 6977 6996 7015 7034 7053 7072 || 63 || 2 4 6 8 9
27 7072 7090 7109 7128 7146 7165 7.183 7202 7220 7238 7.257 || 62 || 2 4 6 7 9
28 7257 7275 7293 7311 7330 7348 7366 7384 7402 74.20 7438 || 61 || 2 4 5 7 9
29 7438 7455 7473 7491 7509 7526 7544 7562 7579 7597 I.7614 || 60° | 2 4 5 7 9
30° | T.7614 7632 7649 7667 7684 7701 7719 7736 7753 7771 7788 || 59 || 2 3 5 7 9
31 7788 7805 7822 7839 7856 7873 7890 7907 7924 7941 7958 || 58 || 2 3 5 7 9
32 7958 7975 7992 8008 8025 8042 8059 8075 8092 8109 8125 || 57 || 2 3 5 7 8
33 81.25 8142 81.58 8175 8191 8208 8224 8241 8257 8274 8290 || 56 || 2 3 5 7 8
34 8290 8306 8323 8339 8355 8371 8388 8404 8420 8436 8452 || 55 || 2 3 5 6 8
35 8452 8468 84.84 8501 8517 85.33 8549 8565 8581 8597 8613 || 54 || 2 3 5 6 8
36 8613 86.29 8644 8660 8676 8692 8708 8724 8740 8755 8771 || 53 || 2 3 5 6 8
37 87.71 8787 8803 88.18 8834 88.50 8865 8881 88.97 8912 8928 || 52 || 2 3 5 6 8
38 8928 8944 8959 8975 8990 9006 9022 9037 9053 9068 9084 || 51 || 2 3 5 6 8
39 9084 9099 9115 9130 9146 9161 9176 9192 9207 9223 T.9238 || 50° | 2 3 5 6 8
40° | I.9238 9254 9269 9284 9300 9315 9330 9346 9361 93.76 9392 || 49 || 2 3 5 6 8
41 93.92 94.07 9422 9438 9453 9468 94.83 9499 9514 95.29 9544 || 48 || 2 3 5 6 8
42 9544. 9560 9575 9590 96.05 9621 9636 9651 9666 9681 96.97 || 47 || 2 3 5 6 8
43 9697 97.12 97.27 9742 9757 9772 9788 9803 98.18 9833 T.9848 || 46 || 2 3 5 6 8
44 || T.9848 9864 9879 9894 9909 9924 9939 9955 9970 9985.ſ0.0000 || 45° | 2 3 5 6 8
45° 0.0000

(24)
Log Tan Log Coºm
.9) .8 Tºnths ſf th9
|→ #–4–4–5 4 3 2 l () Tallaſ Diff}IGICB
0 1 2 3 4 5 #-#= 1 2 3 4 5
0.0000 || 45°
45° | 0.0000 0015 0030 0045 0061 0076 0091 0106 0121 0136 0152 || 44 || 2 3 5 6 8
46 0152 0167 0182 0.197 0212 0228 0243 0258 0273 0288 0303 || 43 || 2 3 5 6 8
47 0303 0319 0334 0349 0364 0379 0395 0410 0425 0440 0456 || 42 2 3 5 6 8
48 0456 0471 0486 0501 0517 0532 0547 0562 0578 0593 0608 || 41 || 2 3 5 6 8
49 0608 0624 0639 0654 0670 0685 0700 0716 0731 0746 0.0762 | 40° i 2 3 5 6 8
50° | 0.0762 0777 0793 0808 0824 0839 0854 0870 0885 0901 0916 || 39 || 2 3 5 6 8
51 0916 0932 0947 0963 0978 0994 1010 1025 1041 1056 1072 38 || 2 3 5 6 8
52 1072 1088 1103 1119 ll35 1150 1166 ll32 1197 1213 1229 || 37 || 2 3 5 6 8
53 1229 1245 1260 1276 1292 1308 1324 1340 1356 1371. 1387 36 || 2 3 5 6 8
54 1387 1403 1419 1435 1451 1467 1483 1499 1516 1532 1548 || 35 || 2 3 5 6 8
55 1548 1564. 1580 1596 1612 1629 1645 1661 1677 1694 1710 || 34 || 2 3 5 6 8
56 1710 1726 1743 1759 1776 1792 1809 1825 1842 1858 1875 || 33 || 2 3 5 7 8
57 1875 1891 1908 1925 1941 1958 1975 1992 2008 2025 2042 || 32 || 2 3 5 7 8
58 2042 2059 2076 2093 2110 2127 2144, 2161 2178 2195 2212 || 31 || 2 3 5 7 9
59 2212 2229 2247 2264 2281 2299 2316 2333 2351 2368 0.2386 || 30° || 2 3 5 7 9
60° l 0.2386 2403 2421 2438 2456 2474 2491 2509 2527 2545 2562 | 29 || 2 4 5 7 9
61 2562 2580 2598 2616 2634 2652 2670 2689 2707 2725 2743 || 28 || 2 4 5 7 9
62 2743 2762 2780 2798 2817 2835 2854 2872 2891 2.910 2928 27 || 2 4 6 7 9
63 2928 2947 2966 2985 3004 3023 3042 306.1 3080 3099 3118 || 26 || 2 4 6 8 9
64 3118 3137 3157 3176 3.196 3215 3235 3254 3274 3294 3313 || 25 || 2 4 6 8 10
65 3313 3333 3353 3373 3393 34.13 3433 3453 3473 3494 3514 24 || 2 4 6 8 10
66 3514 3535 3555 3576 3596 3617 3638 3659 3679 3700 3721 || 23 || 2 4 6 8 10
67 3721 3743 3764 3785 3806 3828 3849 3871 3892 3914 3936 22 || 2 4 6 9 ll
68 3936 3958 3980 4002 4024 4046 4068 4091 4113 4136 41.58 || 21 || 2 4 7 9 ll
69 4158 4181 4204 4227 4250 4273 4296 4319 4342 4366 0.4389 || 20° 2 5 7 10 12
70° 0.4389 4413 4437 4461 4484 4509 4533 4557 4581 4606 4630 | 19 || 2 5 7 10 12
71 4630 4655 4680 4705 4730 4755 4780 4805 4831 4857 4882 18 || 3 5 8 10 13
72 4882 4908 4934 4960 4986 5013 5039 5066 5093 5120 5147 || 17 || 3 5 8 11 13
73 5147 5174 52.01 5229 5256 5284. 5312 5340 5368 5397 5425 | 16 || 3 6 8 11 14
74 5425 5454 5483 5512 5541 5570 5600 5629 5659 5689 5719 || 15 || 3 6 9 12 15
75 57.19 5750 5780 5811 5842 5873 5905 5.936 5968 6000 6032 || 14 || 3 6 9 13 16
76 6032 6065 6097 6130 6163 6.196 6230 6264 6298 6332 6366 || 13 || 3 7 10 13 17
77 6366 6401 6436 6471 6507 6542 6578 6615 6651 J688 6725 | 12 || 4 7 11 14 18
78 6725 6763 6800 6838 6877 6915 6954 6994 7033 7073 7113 || 11 || 4 8 12 16 19
79 7113 7154 7195 7236 7278 7320 7363 7406 7449 7493 0.7537 || 1 (0° || 4 8 13 17 21
80° | 0.7537 7581 7626 7672 7718 7764 7811 7858 7906 7954 8003 9
81 8003 8052 8102 8152 8203 8255 8307 8360 8413 8467 8522 8 TO AWOld interp0-
82 8522 8577 8633 8690 8748 8806 8865 8924 8985 9046 9109 7 || |ātūn in the last
83 9109 9172 9236 9301 9367 9433 95.01 9570 9640 9711 0.9784 6 tºm limbS, USB the
84 || 0.9784 98.57 9932 ſooD& 0085 0164 0244 0326 0409 0494 1.0580 5 || Sp8Glal table On th9
85 | 1,0580 0669 0759 0850 0944 1040 1138 1238 1341 1446 1554 || 4 "º.
86 1554 1664. 1777 1893 2012 2135 2261 2391. 2525 2663 2806 3 DOlát0m WOuld ſiſt
87 2806 2954 31.06 3264 3429 3599 3777 3962 4155 4357 4569 * I is aminate in the
88 4569 4792 5027 5275 5539 5819 6119 6441 6789 7167 1.7581 *., last tiss mes)
89 | 1.7581 8038 8550 9130 9800ſ2.0591 1561 2810 4571 7581 co Oo º
90° OO


(25)
Log Tan
\ L O G # & log sin & log cos 7
Log Coſtan
|-º-º-º: 6 5 4
0 1 2 3TA-5 #–4–4–1, 0
so.o. 0.7537 7541 7546 7550 7555 7559 7563 7568 7572 7577 0.7581
80.1
80.2
80.3
80.4
80.5
80.6
80.7
80.8
80.9
7581 7586 7590 7595 7599 7604. 7608 7613 7617 7622 7626
7626 7631 7635 7640 7644 7649 7654. 7658 7663 7667 7672
7672 7676 7681 7685 7690 7695 7699 7704 7708 7713 7718
7718 7722 7727 7731 7736 7741 7745 7750 7755 7759 7764
7764 7769 7773 7778 7783 7787 7792 7797 7801 7806 7811
7811 7815 7820 7825 7830 7834 7839 7844. 7849 7853 7858
7858 7863 7868 7872 7877 7882 7887 7891 7896 7901 7906
7906 7911 7915 7920 7925 7930 7935 7940 7944. 7949 7954
7954 7959 7964 7969 7974 7978 7983 7988 7993 7998 0.8003
81°.0l O.8003 8008 8013 8018 8023 8027 8032 8037 8042 8047 8052
81.1
81.2
81.3
81.4
81.5
81.6
81.7
81.8
81.9
8052 8057 8062 8067 8072 8077 8082 8087 8092 8097 8102
8102 8107 8112 8117 8122 8127 81.32 8137 8142 8147 8152
8152 81.58 8163 8168 8173 8178 8183 8188 8.193 8198 8203
8203 8209 82.14 8219 8224 8229 8234 8239 8245 8250 8255
8255 8260 8265 8271 8276 8281 8286 8291 8297 8302 8307
8307 8312 8318 8323 8328 8333 8339 8344 8349 8355 8360
8360 8365 8371 8376 8381 8387 8392 8397 8403 8408 8413
8413 84.19 8424 8,429 8435 8440 8446 8451 8456 8462 8467
8467 8473 8478 8484 8489 8495 8500 8506 8511 8516 0.8522
s2.0 0.8522 8527 85.33 8539 8544 85.50 8555 8561 8566 8572 8577
82.1
82.2
82.3
82.4
82.5
82.6
82.7
82.8
82.9
83°.0
83.1
83.2
83.3
83.4
83.5
83.6
83.7
83.8
83.9
84°.0
84.1
84.2
84.3
84.4
84.5
84.6
84.7
84.8
84.9
|
8577 8583 8588 8594 8600 8605 8611 8616 8622 8628 86.33
8633 8639 8645 8650 8656 8662 8667 8673 86.79 8684 8690
8690 8696 8701 8707 8713 8719 8724 8730 8736 8742 8748
8748 8753 8759 8765 8771 8777 8782 8788 8794 8800 8806
8806 88.12 8817 8823 8829 8835 8841 8847 8853 8859 8865
8865 8871 8877 8883 8888 8894. 8900 8906 8912 8918 8924
8924 8930 8936 8942 8949 8955 8961 8967 8973 8979 8985
8985 8991 8997 9003 9009 9016 9022 9028 9034 9040 9046
9046 9053 9059 9065 90.71 9077 9084 9090 9096 9102 0.9109
0.9109 91.15 9121 9127 9134 91.40 9146 9153 9159 91.65 9172
9172 91.78 91.84 9191 91.97 92.04 9210 92.16 9223 92.29 9236
9236 9242 92.49 92.55 92.62 9268 9275 9281 9288 9294 9301
9301 9307 9314 93.20 9327 9333 9340 9347 9353 9360 9367
9367 93.73 9380 9386 93.93 9400 9407 9413 9420 9427 9433
9433 94.40 9447 9454 9460 94.67 9474 9481 9488 9494. 95.01
9501 9508 9515 9522 95.29 9536 9543 9549 95.56 9563 9570
9570 95.77 9584 9591 95.98 9605 96.12 96.19 9626 9633 9640
9640 9647 9654 9662 9669 96.76 9683 9690 96.97 9704. 9711
9711 9719 97.26 9733 97.40 97.47 97.55 9762 9769 97.77 0.9784
0.9784. 9791 97.98 9806 98.13 98.20 98.28 9835 98.43 98.50 98.57
98.57 98.65 98.72 9880 98.87 98.95 9.902 99.10 99.17 99.25 0.9932
0.9932 99.40 99.47 9955 9962 99.70 9978 9985 9993 ſooDO 1.0008
1.0008 0016 0023 0031 0039 0047 0054 O062 O070 0078 0085
0085 0093 0.101 0109 0.117 0125 0133 0140 0148 0.156 0164
0.164 0172 0180 0188 0.196 0204 0212 0220 0228 0236 0244
0244 0253 0261 0269 O277 0285 0293 0301 0310 0318 O326
0326 0334 0343 0351 0359 0367 O376 0384 0392 0401 0409
0409 0418 0426 0435 0443 0451 0460 0468 0477 0485 0494
1.0494 0503 0511 0520 0528 0537 0546 0554 0563 0572 1.0580
9.9
9.8
9.7
9.6
9.5
9.4
9.3
9.2
9.1
9°.()
8.9
8.8
8.7
8.6
8.5
8.4
8.3
8.2
8.1
S*. ()
7.9
7.8
7.7
7.6
7.5
7.4
7.3
7.2
7.1
79.0
6.9
6.8
6.7
6.6
6.5
6.4
6.3
6.2
6.1
(6°.()
5.9
5.8
5.7
5.6
5.5
5.4
5.3
5.2
5.1
5°.()
(26)
Tºnths Of th9
Tallaſ Diff}[Bſ100
1 2 3 4 5


Log Tan Log Cotan
E-T-TE 4 3 2 YTº
0 Ti-3-3-#–E–4–3 & 0 |º:
85°.0 1.0580 0589 0598 0607 0616 0624 0633 0642 0651 0660 1.0669 || 4.9
85.1 || 0669 0678 0687 0695 0704 0713 0722 0731 0740 0750 0759 4.8
85.2 || 0759 0768 0777 0786 0795 0804 0814 0823 0832 0841 0850 4.7
85.3 || 0850 0860 0869 0878 0888 0897 0907 0916 0925 0935 0944 4.6
85.4 || 0944 0954 0963 0973 0982 0992 1002 1011 1021 1030 1040 || 4.5
85.5 1040 1050 1060 1069 1079 1089 1099 1109 1118 1128 1138 4.4
85.6 1138 1148 1158 1168 1178 1188 1198 1208 1218 1228 1238 || 4.3
85.7 1238 1249 1259 1269 1279 1289 1300 1310 1320 1331 1341 4.2
85.8 1341 1351 1362. 1372 1383 1393 1404 1414 1425 1435 1446 || 4.1
85.9 1446 1457 1467 1478 1489 1499 1510 1521 1532 1543 1.1554 4°.()
86°.0i 1.1554 1564 1575 1586 1597 1608 1619 1630 1642 1653 1664 | 3.9
86.1 1664. 1675 1686 1698 1709 1720 1731. 1743 1754, 1766 1777. 3.8
86.2 1777 1788 1800 1812 1823 1835 1846 1858 1870 1881 1893 3.7
86.3 1893 1905 1917 1929 1941 1952 1964. 1976 1988 2000 2012 || 3.6
86.4 2012 2025 2037 2049 2061 2073 2086 2098 2110 2123 2135 | 3.5
86.5 2135 2148 2160 2173. 2185 2198 2210 2223 2236 2249 2261 : 3.4
86.6 2261 2274. 2287 2300 2313 2326 2339 2352 2365 2378 2391 i 3.3
86.7 2391 2404 2418 2431 2444 2458 2471 2485 2498 2512 2525 || 3.2
86.8 2525 2539 2552 2566 2580 2594 2608 2621 2635 2649 2663 3.1
86.9 2663 2677 2692 2706 2720 2734 2748 2763 2777 2792 1.2806 || 3°.()
87°.0l 1.2806 2821 2835 2850 2864. 2879 2894 2.909 2924 2939 2954 || 2.9
87.1 2954 2969 2984 2999 3014 3029 3044 3060 3075 3091 3106 || 2.8
87.2 3106 3122 3137 3153 3169 3185. 3200 3216 3232 3248 3264 || 2.7
87.3 3264 3281 3297 3313 3329 3346. 3362 3379 3395 3412 3429 2.6
87.4 3429 3445 3462 3479 3496 3513 3530 3547 3564. 3582 3599 2.5
87.5 3599 36.16 3634 3652 3669 3687 3705 3723 3740 3758 3777 2.4
87.6 3777 3795 3813 3831 3850 3868 3887 3905 3924 3943 3962 2.3
87.7 3962 3981 4000 4019 4038 4057 4077 4096 4116 4135 4155 || 2.2 8 10
87.8 4155 4175 4195 4215 4235 4255 4275 42.95 4316 4336 4357 || 2.1 8 10
87.9 4357 4378 4399 4420 4441 4462 4483 4504 4526 4547 1.4569 2°.() 8 ll
88°.0| 1.4569 4591 4613 4635 4657 4679 4702 4724 4747 4769 4792 | 1.9 9 11
88.1 4792 4815 4838 4861 4885 4908 4932 4955 4979 5003 5027 | 1.8 9 12
88.2 5027 5051 5076 5100 5125 5149 5174 5199 5225 5250 5275 : 1.7 7 10 12
88.3 5275 5301 5327 5353 5379 5405 5432 5458 5485 5512 5539 1.6 8 11 13
88.4 5539 5566 5594 5621 5649 5677 5705 5733 5762 5790 5819 || 1.5 8 11 14
88.5 5819 5848 5878 5907 5937 5967 5997 6027 6057 6088 6119 || 1.4 6 9 12 15
88.6 6119 6150 6182 6213 6245 6277 6309 6342 6375 6408 6441 || 1.3 6 10 13 16
88.7 6441 64.75 6508 6542 6577 6611 6646 6682 6717 6753 6789 || 1.2 7 10 14 17
88.8 6789 6825 6862 6899 6936 6974 7012 7050 7088 7127 7.167 | 1.1 8 ll 15 19
88.9 7167 7206 7246 7287 7328 7369 7410 7452 7495 7538 1.7581 | 19. (O)
sºlo 1.7581 7624 7669 7713 7758 7804 7850 7896 7943 7990 8038 || 0.9 TD AWDiſlinterp0-
89.1 | 8038 8087 8136 8186 8236 8287 8338 8390 8443 8496 85.50 0.8 llation in the last
89.2 | 85.50 8605 8660 8716 8773 8830 8889 8948 9008 9068 9130 0.7 | Bleſſ liſles, USB
89.3 || 9130 9193 9256 93.20 9386 9452 9519 9588 9657 9728 1.9800 || 0.6 | ſiſt in the tailſ. Of
89.4 | 1.9800 9873 9947ſoo22 0099 0177 0257 0338 0421 0505 2.0591 || 0.5 | |0gaſitims of ſlum-
89.5 || 2.0591 0679 0769 O860 0954. 1049 1147 1246 1349 1453 1561 || 0.4 "ºn intBr-
896 || 1:6, 167; 1733 1899 2013 2,42 22% 23%. 239 36%. 2810 || 93 || mºnt
89.7 2810 2957 3110 3268 3431 3602 3779 3964 4157 4359 .4571 0.2 | . . .
89.8 || 457, 4794 5028 5277 5549.5829 6120 642 6739 7.167 2,7581 || 0,1 || stiºn.)
89.9 || 2.7581 8039 8550 9130 9800ſ?.0592 1561 2810 4571 7581 co || 0°.O s


(27)
Condensed Table of Trigonometric Functions
° Rădăll sin tan sec vers ° Rădă|| sin tan sec vers
O° 0.0000 || 0.0000 0.0000 1,000 0.0000 |90° | |45° 0.785| 0.707 1.000 1.414 0.293 |45°
1 .0175 | .0175 .0175 1.000 .0002 | 89 46 .803 | .719 1.036 1.440 .305 || 44
2 .0349 .0349 .0349 1.001 .0006 || 88 47 .820 .731 1.072 1,466 .318 || 43
3 .0524 .0523 .0524 1,001 .0014 | 87 48 .838 .743 1.111 1,494 .331 || 42
4 .0698 .0698 .0699 1.002 .0024 || 86 49 .855 | .755 1.150 1.524 .344 || 41
5° 0.0873 || 0.0872 0.0875 1,004 0.0038 85° | |50° 0.873 || 0.766 1.192 1.556 0.357 |40°
6 .1047 .1045 .1051 1,006 .0055 | 84 51 .890 | .777 1,235 1,589 .371 39
7 .1222 | . 1219 .1228 1,008 .0075 | 83 52 .908 .788 1.280 1.624 .384 || 38
8 . 1396 | . 1392 .1405 1,010 .0097 || 82 53 .925 | .799 1,327 1,662 .398 || 37
9 .1571 .1564 .1584 1,012 .0123 81 54 .942 .809 1,376 1,701 .412 || 36
10° 0.1745 0.1736 0.1763 1.015 0.0152 |30° 55° 0,960 0.819 1.428 1.743 0.426 35°
11 .1920 .1908 .1944 1,019 .0184 79 56 .977 .829 1,483 1,788 .441 || 34
12 .2094 | .2079 .2126 1,022 .0219 || 78 57 0.995 | .839 1.540 1.836 .455 33
13 .2269 .2250 .2309 1,026 .0256 77 58 1,012 .848 1,600 1.887 .470 || 32
14 .2443 | .2419 .2493 1.031 .0297 || 76 59 1,030 .857 1,664 1.942 .485 || 31
15° 0.262 0.259 0.268 1,035 0.0341 || 75° | | 60° 1,047| 0.866 1,732 2.00 0.500 30°
16 .279 .276 .287 1,040 .0387 74 61 1,065 | .875 1.804 2.06 .515 29
17 .297 .292 .306 1,046 .0437 | 73 62 l,082 | .883 1,881 2.13 .531 28
18 .314 | .309 .325 1.051 .0489 || 72 63 1.100 | .891. 1,963 2.20 .546 27
19 .332 .326 .344 1,058 .0545 71 64 1.117 | .899 2,050 2.28 .562 26
20° 0.349 || 0.342 0.364 1.064 0.0603 |70° 65° 1,134 || 0.906 2.14 2.37 0.577 || 25°
21 .367 .358 .384 1,071 .0664 || 69 66 1.152 | .914 2.25 2.46 .593 24
22 .384 .375 .404 1,079 .0728 68 67 1,169 .921 2.36 2.56 .609 || 23
23 .401 | .391 .424 1,086 .0795 || 67 68 1.187 | .927 2.48 2.67 .625 22
24 .419 .407 .445 1.095 .0865 | 66 69 l.204 | .934 2.61 2.79 .642 21
25° 0.436 0.423 0.466 1.103 0.0937 65° || ||70° 1.222 0.940 2.75 2.92 0.658 |20°
26 .454 .438 .488 1.113 .1012 | 64 71 1.239 .946 2.90 3.07 .674 19
27 .471 .454 .510 1,122 .1090 63 72 1.257 | .951 3,08 3.24 .691 | 18
28 .489 | .469 .532 1.133 .1171 62 73 1.274 .956 3.27 3.42 .708 17
29 .506 | .485 .554 1.143 .1254 61 74 1.292 | .961 3.49 3.63 .724 | 16
30° 0.524 0.500 0.577 1.155 0.1340 |60° 75° 1.309 || 0.966 3.73 3.86 0.741 15°
31 .541 .515 .601 1,167 .1428 59 76 1,326 .970 4.01 4.13 .758 14
32 .559 .530 .625 1.179 .1520 58 77 1.344 .974 4.33 4.45 .775 13
33 .576 .545 .649 1.192 .1613 || 57 78 1.361 | .978 4.70 4.81 .792 | 12
34 .593 .559 .675 1,206 .1710 || 56 79 1,379 | .982 5.14 5.24 .809 || 11
35° 0.611 0.574 0.700 1.221 0.1808 || 55° | |80° 1.396 || 0.985 5.67+ 5.76% 0.826 10°
36 .628 .588 .727 1.236 .1910 || 54 81 1.414 .988 6.31% 6.39% .844 9
37 .646 .602 .754 1.252 .2014 || 53 82 1.431 .990 7.12+ 7.19% .861 || 8
38 .663 | .616 .781 1.269 .2120 | 52 83 1.449 .993 8.14% 8.21+ .878 7
39 .681 .629 .810 1,287 .2229 || 51 84 1,466 .995 9.51% 9.57% .895 6
40° 0.698 || 0.643 0.839 1.305 0.234 50° 85° 1.484 || 0.996 11.43+ 11.47% 0.913 5°
41 .716 .656 .869 1.325 .245 || 49 86 1.501 | .998 14.30+ 14.34% .930 || 4
42 .733 .669 .900 1,346 .257 || 48 87 1.518 .999 19.08%. 19.11% .948 || 3
43 .750 | .682 .933 1.367 .269 || 47 88 1.536 0.999 28.64%. 28.65% .965 2
44 .768 . .695 0.966 1.390 .281 || 46 89 1.553 | 1.000 57.29%. 57.30% 0.983 1
45° 0.785 0.707 1.000 1,414 0.293 |45° | | 90° 1.571 | 1,000 co co 1.000 || 0°
COS Ctm CSC CVI’s O cos cºm cºc cyms | *
*Interpolation at points marked * may be inaccurate


... -...--~~~~~
…seaeº
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